{
"cells": [
{
"cell_type": "markdown",
"id": "8e66b3cd-54eb-4b93-a3c8-e6a33952b33e",
"metadata": {},
"source": [
"Math 420/620 Quiz 10"
]
},
{
"cell_type": "markdown",
"id": "d85a6029-da79-4bea-8145-8775de2a5e29",
"metadata": {},
"source": [
"1. A squadron of 16 bombers needs to penetrate air defenses to reach its\n",
"target. They can either fly low and expose themselves to the air defense\n",
"guns, or fly high and expose themselves to surface–to–air missiles. In\n",
"either case, the air defense firing sequence proceeds in three stages. First,\n",
"they must detect the target, then they must acquire the target (lock on\n",
"target), and finally they must hit the target. Each of these stages may or\n",
"may not succeed. The probabilities are as follows:\n",
"\n",
"|AD Type|Pdetect|Pacquire|Phit|\n",
"|:-:|:-:|:-:|:-:|\n",
"|Low|0.90|0.80|0.05|\n",
"|High|0.75|0.95|0.70|\n",
"\n",
"The guns can fire 20 shells per minute, and the missile installation can\n",
"fire three per minute. The proposed flight path will expose the planes for\n",
"one minute if they fly low, and five minutes if they fly high."
]
},
{
"cell_type": "markdown",
"id": "bab46c1c-0ed5-4b87-ac4b-4f79cae65411",
"metadata": {},
"source": [
"(i) Determine the optimal flight path (low or high). The objective is to\n",
"maximize the bombers that survive to strike the target."
]
},
{
"cell_type": "markdown",
"id": "143235f2-dd9a-4a35-b3a6-1a589fdf014f",
"metadata": {},
"source": [
"For the low flying planes define\n",
"\n",
"- $t_L=1$ the time in minutes the low-flying plane is exposed to defensive fire.\n",
"- $r_L=20$ the number of shells fired on low-flying planes per minute.\n",
"- $p_L$ the probability a shell hits a low-flying plane.\n",
"- $S_L$ the number of low-flying planes that survive.\n",
"\n",
"and for the high-flying planes\n",
"\n",
"- $t_H=5$ the time in minutes the high-flying plane is exposed to defensive fire.\n",
"- $r_H=3$ the number of missles fired on high-flying planes per minute.\n",
"- $p_H$ the probability a missle hits a high-flying plane.\n",
"- $S_H$ the number of high-flying planes that survive."
]
},
{
"cell_type": "markdown",
"id": "00fdc50a-e5f2-435b-bd05-7608245316fa",
"metadata": {},
"source": [
"We assume that the probabilities are independent so that\n",
"$$\n",
" q_a=P_{\\rm detect} \\cdot P_{\\rm acquire} \\cdot P_{\\rm hit}\n",
"$$\n",
"where the altitude $a\\in \\{L, H\\}$ and the values for $P_{\\rm detect}, P_{\\rm acquire}$ and $P_{\\rm hit}$\n",
"are given by the corresponding line in the table."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "7d9b0272-046f-4096-86ee-59c3acb9ed9d",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.036000000000000004"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pL=0.90*0.80*0.05"
]
},
{
"cell_type": "markdown",
"id": "a396f100-dcd0-48de-8d88-3737de7f5711",
"metadata": {},
"source": [
"Since the enemy doesn't fire at planes which are already\n",
"shot down, every shell is assumed to be shot at a plane\n",
"that is still flying.\n",
"If the defenders run out of planes to fire at they stop\n",
"shooting.\n",
"Over $t_L$ minutes a total of $t_Lr_L=20$ shells\n",
"are fired."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "3725b97a-d555-4bc6-9d88-e5beb9aa05ce",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"20"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tL=1; rL=20; tL*rL"
]
},
{
"cell_type": "markdown",
"id": "d1b716a1-b111-44cc-9527-c0b578a50e30",
"metadata": {},
"source": [
"Let $X_i$ be a random variable equal to 1 if a shell number $i$ hits\n",
"the target and 0 if it misses. Assuming each shell is independently\n",
"targeted, we have\n",
"$$\n",
" X_i=\\cases{1 & with probability $p_L$\\cr 0 & with probability $1-p_L$}\n",
" \\qquad\\hbox{for}\\qquad i=1,2,\\ldots,20.\n",
"$$\n",
"If there were an infinite number of planes, the total number of low-flying planes shot down would be\n",
"$$\n",
" T_L=\\sum_{i=1}^{20} X_i.\n",
"$$\n",
"Let $S_L$ be how many out of the $16$ planes survive. Therefore\n",
"$$\n",
" S_L=\\cases{\n",
" 0 & with probability ${\\bf P}\\{ T_L\\ge 16 \\}$\\cr\n",
" n & with probability ${\\bf P}\\{ T_L=16-n \\}$.\n",
" }\n",
"$$\n",
"Here $n=1,2,\\ldots,16$.\n",
"The expected number that survive is\n",
"$$\n",
" {\\bf E}[S_L]=\\sum_{n=1}^{16} n{\\bf P}\\{ T_L=16-n \\}.\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "e0b14c81-3ee5-4b69-8e98-59d90c2847e2",
"metadata": {},
"source": [
"Since $T_L$ is a sum of independent Bernoulli random\n",
"variables it has a binomial distribution. Therefore\n",
"$$\n",
" {\\bf P}\\{ T_L=m \\} = {20\\choose m} p_L^m(1-p_L)^{20-m}.\n",
"$$\n",
"It follows that\n",
"$$\n",
" {\\bf E}[S_L]=\\sum_{n=1}^{16} n{20\\choose 16-n} p_L^{16-n}(1-p_L)^{4+n}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "3f383dd8-a5c9-4287-a809-bcb29229f166",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"15.27999999999999"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"PTL(m)=binomial(20,m)*pL^m*(1-pL)^(20-m)\n",
"ESL=sum(n*PTL(16-n) for n=1:16)"
]
},
{
"cell_type": "markdown",
"id": "9f124d80-2a36-49ee-8573-3bb14329120e",
"metadata": {},
"source": [
"Note that an altermate way to approximate the same value is\n",
"to assume the probability that all planes are shot down\n",
"is vanishingly small."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "a35697eb-f356-44a0-b72c-4b8f84e217f2",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2.9443114378667005e-22"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"QTL16=sum(PTL(n) for n=17:20)"
]
},
{
"cell_type": "markdown",
"id": "8f2479df-e0e2-48ad-af7d-4ee5f4df8052",
"metadata": {},
"source": [
"Thus, $P\\{T_L> 16\\} \\approx 2.9443114378667005\\times 10^{-22}$ implies\n",
"$$\n",
" {\\bf P}\\{ T_L \\le 16\\} = 1 - P\\{T_L> 16\\} \\approx 1\n",
"$$\n",
"Since\n",
"$$\n",
" S_L=\\cases {\n",
" 0 & for $T_L> 16$\\cr\n",
" 16-T_L & for $T_L\\le 16$,\n",
" }\n",
"$$\n",
"it follows that\n",
"$$\n",
" {\\bf E}[S_L]={\\bf E}[16-T_L] {\\bf P}\\{T_L\\le16\\}\n",
" \\approx 16-{\\bf E}[T_L].\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "1e4ee58b-a4f0-4305-a551-c450c330cc0c",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.7200000000000001"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"20*pL"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "34173444-c8a3-466b-b3a1-1ef31db457b4",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"15.28"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"16-20*pL"
]
},
{
"cell_type": "markdown",
"id": "9f9cb43b-2cc6-4fac-9f55-5ca22fae72fb",
"metadata": {},
"source": [
"Computing\n",
"$$\n",
" {\\bf E}[T_L]=\\sum_{i=1}^{20} {\\bf E}[X_i]= 20p_L\\approx 0.72\n",
"$$\n",
"yields that\n",
"$$\n",
" {\\bf E}[S_L]\\approx 15.28.\n",
"$$\n",
"Note that in spite of dropping the small term, numerically, this turns out to the\n",
"same as the previously computed answer."
]
},
{
"cell_type": "markdown",
"id": "5e521393-419a-4973-8bea-ac7b7ba89da9",
"metadata": {},
"source": [
"Now perform a similar analysis for the high-flying planes."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "0793033c-8fea-4c84-9616-47e0b94a9074",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.4987499999999999"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pH=0.75*0.95*0.70"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "08769e87-f6e2-46bb-b469-22a77f1d6728",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"15"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tH=5; rH=3; tH*rH"
]
},
{
"cell_type": "markdown",
"id": "f61aceb2-1ac3-4683-85f5-762396876910",
"metadata": {},
"source": [
"Let $Y_i$ be a random variable equal to 1 if a missle number $i$ hits\n",
"the target and 0 if it misses. Assuming each missle is independently\n",
"targeted, we have\n",
"$$\n",
" Y_i=\\cases{1 & with probability $p_H$\\cr 0 & with probability $1-p_H$}\n",
" \\qquad\\hbox{for}\\qquad i=1,2,\\ldots,15.\n",
"$$\n",
"If there were an infinite number of planes, the total number of high-flying planes shot down would be\n",
"$$\n",
" T_H=\\sum_{i=1}^{15} Y_i.\n",
"$$\n",
"Let $S_H$ be how many out of the $16$ planes survive. Therefore\n",
"$$\n",
" S_H=\\cases{\n",
" 0 & with probability $0$\\cr\n",
" n & with probability ${\\bf P}\\{ T_H=16-n \\}$.\n",
" }\n",
"$$\n",
"Here $n=1,2,\\ldots,16$.\n",
"The expected number that survive is\n",
"$$\n",
" {\\bf E}[S_H]=\\sum_{n=1}^{16} n{\\bf P}\\{ T_H=16-n \\}.\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "58d45e0a-7478-42fc-bb64-d114158dc968",
"metadata": {},
"source": [
"Since $T_H$ is a sum of independent Bernoulli random\n",
"variables it has a binomial distribution. Therefore\n",
"$$\n",
" {\\bf P}\\{ T_H=m \\} = {15\\choose m} p_H^m(1-p_H)^{15-m}.\n",
"$$\n",
"It follows that\n",
"$$\n",
" {\\bf E}[S_H]=\\sum_{n=1}^{16} n{20\\choose 16-n} p_L^{16-n}(1-p_L)^{n-1}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "e7a943b9-52e3-46d6-bd0f-5a2f602a22e5",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"8.518750000000002"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"PTH(m)=binomial(15,m)*pH^m*(1-pH)^(15-m)\n",
"ESH=sum(n*PTH(16-n) for n=1:16)"
]
},
{
"cell_type": "markdown",
"id": "91eb28fd-099d-4136-9502-59ee23f41f88",
"metadata": {},
"source": [
"The alternative method of computing ${\\bf E}[S_H]$ is\n",
"even easier and exact in this case because there is no chance that\n",
"all the planes get shot down by missiles."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "64f65eb2-17c4-4431-8f52-26a5ca920e64",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"7.481249999999998"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"15*pH"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "76323893-bc3a-40da-9a91-8b11e97e25d8",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"8.51875"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"16-15*pH"
]
},
{
"cell_type": "markdown",
"id": "f5fa72d5-44cb-47f5-832d-11a9fa38c1d9",
"metadata": {},
"source": [
"It follows that\n",
"$$\n",
" {\\bf E}[S_H]=16-{\\bf E}[T_H]=16-15*p_H\\approx 8.51875\n",
"$$\n",
"which is the same as computed above."
]
},
{
"cell_type": "markdown",
"id": "735c3636-e2ac-41e7-8bb6-f6f654023720",
"metadata": {},
"source": [
"In summary\n",
"$$\n",
" {\\bf E}[S_L]=15.28\\qquad\\hbox{and}\\qquad\n",
" {\\bf E}[S_H]=8.519.\n",
"$$\n",
"Therefore, \n",
"the optimal path is to fly low so that on average $15.28$ survive to strike the target."
]
},
{
"cell_type": "markdown",
"id": "ddb0046b-89ea-41be-9d11-898dde18bebf",
"metadata": {},
"source": [
"(ii) Each individual bomber has a 70 percent chance to destroy the target. Use\n",
"the results of part (i) to determine the chances of success (target\n",
"destroyed) for this mission."
]
},
{
"cell_type": "markdown",
"id": "7fb8c610-d58b-4e55-a81a-24a7b2262b23",
"metadata": {},
"source": [
"Assume success means destroying the target. Let\n",
"\n",
"- $p_D=0.7$ be the probability that an individual plane destroys the target.\n",
"\n",
"We want to compute\n",
"$$\n",
" {\\bf P}\\{\\hbox{success}\\}=\\sum_{n=1}^{16} {\\bf P}\\big\\{\\hbox{success}|S_L=n\\big\\}{\\bf P}\\{S_L=n\\}\n",
"$$\n",
"Suppose $S_L=n$ planes get through the defenses. Let $Z_i$ be a random\n",
"variable equal to $1$ if plane $i$ hits the target and $0$ if not. Assuming\n",
"each of the planes which get through have an independent chance of success,\n",
"we have\n",
"$$\n",
" Z_i=\\cases{1 & with probability $p_D$\\cr 0 & with probability $1-p_D$.}\n",
" \\qquad\\hbox{for}\\qquad\n",
" i=1,2,\\ldots,n.\n",
"$$\n",
"We want to compute the probability that at least one plane which gets through\n",
"also hits the target. Thus\n",
"$$\n",
" {\\bf P}\\{\\,Z_i=1\\hbox{ for at least one $i$} | S_L=n\\,\\}\n",
" =1-{\\bf P}\\{\\,Z_i=0\\hbox{ for all $i$}|S_L=n\\,\\}.\n",
"$$\n",
"By independence\n",
"$$\n",
" {\\bf P}\\{\\,Z_i=0\\hbox{ for all $i$}|S_L=n\\,\\}=\\prod_{i=1}^{n} {\\bf P}\\{Z_i=0\\}\n",
" =(1-p_D)^n.\n",
"$$\n",
"Therefore\n",
"$$\n",
" {\\bf P}\\big\\{\\hbox{success}|S_L=n\\big\\}=1-(1-p_D)^n\n",
"$$\n",
"combined with the fact from earlier that\n",
"$$\n",
" {\\bf P}\\{S_L=n\\}={20\\choose 16-n} p_L^{16-n}(1-p_L)^{4+n}\n",
"$$\n",
"yields\n",
"$$\n",
" {\\bf P}\\{\\hbox{success}\\}=\\sum_{n=1}^{16}\\big(1-(1-p_D)^n\\big){20\\choose 16-n} p_L^{16-n}(1-p_L)^{4+n}.\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "dbd7efee-573e-4ee7-bf67-cfb9b0599833",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.7"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pD=0.7"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "22a35530-0fee-4201-99af-b7aea0a78233",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.9999999783964197"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Psuccess=sum((1-(1-pD)^n)*PTL(16-n) for n=1:16)"
]
},
{
"cell_type": "markdown",
"id": "3b390245-2033-4f38-a80b-9870e01ca931",
"metadata": {},
"source": [
"Therefore, there is a $99.9999978$ percent chance of mission success."
]
},
{
"cell_type": "markdown",
"id": "4a41deba-eb1e-4684-97e7-72d06915d786",
"metadata": {},
"source": [
"(iii) Determine the minimum number of bombers necessary to guarantee\n",
"a 95\\% chance of mission success."
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "781bdb53-afe2-45a5-b240-08ef1239f2af",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Ps (generic function with 1 method)"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Ps(m)=sum((1-(1-pD)^n)*PTL(m-n) for n=1:m)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "71e71ec5-390f-46d5-a92e-e95334b88f24",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"┌────────┬────────────┐\n",
"│\u001b[1m planes \u001b[0m│\u001b[1m P(success) \u001b[0m│\n",
"├────────┼────────────┤\n",
"│ 1 │ 0.336232 │\n",
"│ 2 │ 0.688229 │\n",
"│ 3 │ 0.882921 │\n",
"│ 4 │ 0.961291 │\n",
"│ 5 │ 0.987971 │\n",
"│ 6 │ 0.996353 │\n",
"│ 7 │ 0.998903 │\n",
"│ 8 │ 0.999671 │\n",
"│ 9 │ 0.999901 │\n",
"│ 10 │ 0.999970 │\n",
"│ 11 │ 0.999991 │\n",
"│ 12 │ 0.999997 │\n",
"│ 13 │ 0.999999 │\n",
"│ 14 │ 1.000000 │\n",
"│ 15 │ 1.000000 │\n",
"│ 16 │ 1.000000 │\n",
"└────────┴────────────┘\n"
]
}
],
"source": [
"using PrettyTables\n",
"T=[1:16 Ps.(1:16)]\n",
"pretty_table(T,\n",
" formatters=[fmt__printf(\"%3d\",[1]),fmt__printf(\"%.6f\",[2])],\n",
" column_labels=[\"planes\",\"P(success)\"])"
]
},
{
"cell_type": "markdown",
"id": "121cba6f-7896-4fa8-a191-8aabd8342f84",
"metadata": {},
"source": [
"It follows that $4$ airplanes leads to a 96% chance of mission success\n",
"but $3$ only provides a 88% chance of success. Thus, $4$ is the minimum\n",
"necessary to guarantee at least a 95% chance of success."
]
},
{
"cell_type": "markdown",
"id": "ef363731-6fee-42cc-87ac-f5b5fabc87ea",
"metadata": {},
"source": [
"(iv) Perform a sensitivity analysis with respect to the probability \n",
"$p = 0.7$ that an individual bomber can destroy the target. Consider the\n",
"number of bombers that must be sent to guarantee a 95\\% chance of\n",
"mission success."
]
},
{
"cell_type": "markdown",
"id": "acb1b7b0-d267-4ed4-8860-57e7f04ae593",
"metadata": {},
"source": [
"Let $N(p)$ be the minimum number of planes needed to guarantee a 95\\% chance of mission success.\n",
"Since this is a discrete function, we plug in different values for $p$,\n",
"recompute the table in the previous part and then automatically\n",
"search for the minimum number of planes in a squadron for which\n",
"${\\bf P}\\{\\hbox{success}\\}\\ge 0.95.$"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "72e4b507-1817-41e0-a953-f5d38b2f667f",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"N95 (generic function with 1 method)"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Ps(p,m)=sum((1-(1-p)^n)*PTL(m-n) for n=1:m)\n",
"Tp(p)=[Ps(p,m) for m=1:16]\n",
"N95(p)=findfirst(x->x>0.95,Tp(p))"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "c2543d4c-ee72-46a0-9f63-19ee6e0d93df",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Check that 0.7 still returns 4 planes \n",
"N95(0.7)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "a82d11a3-2e45-4d37-99c8-5d9c7c59fb71",
"metadata": {},
"outputs": [],
"source": [
"using Plots"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "0bbbc53d-c576-4cdb-afd6-14702672f042",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
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\")
"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(N95,0.18:0.0005:1.0,title=\"Planes needed for 95 Chance of Success\",\n",
" xlabel=\"Probabilty p to hit target\",ylabel=\"N planes\",legend=false)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "21394d6f-0084-4ba5-aa4b-2c1b9ceee9c4",
"metadata": {},
"outputs": [],
"source": [
"T2=[0.2:0.1:1.0 N95.(0.2:0.1:1.0)];"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "4b01a7b8-19bf-4409-b563-fb51b60de3ff",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"┌─────┬──────┐\n",
"│\u001b[1m p \u001b[0m│\u001b[1m N(p) \u001b[0m│\n",
"├─────┼──────┤\n",
"│ 0.2 │ 15 │\n",
"│ 0.3 │ 10 │\n",
"│ 0.4 │ 7 │\n",
"│ 0.5 │ 6 │\n",
"│ 0.6 │ 5 │\n",
"│ 0.7 │ 4 │\n",
"│ 0.8 │ 4 │\n",
"│ 0.9 │ 4 │\n",
"│ 1.0 │ 3 │\n",
"└─────┴──────┘\n"
]
}
],
"source": [
"pretty_table(T2,\n",
" formatters=[fmt__printf(\"%.1f\",[1]),fmt__printf(\"%d\",[2])],\n",
" column_labels=[\"p\",\"N(p)\"])"
]
},
{
"cell_type": "markdown",
"id": "ea4b6875-0ba9-4227-b6a7-ea2bc34ac44e",
"metadata": {},
"source": [
"(iv) Bad weather reduces both $P_{\\rm detect}$ and $p$, the \n",
"probability that a bomber\n",
"can destroy the target. If all of these probabilities are reduced in the\n",
"same proportion, which side gains an advantage in bad weather?"
]
},
{
"cell_type": "markdown",
"id": "026bc8aa-90fc-4e14-aa0a-9e617164b082",
"metadata": {},
"source": [
"Let $\\gamma$ be the proportion by which the probabilities are reduced. Write\n",
"$\\gamma p_L$ and $\\gamma p_D$ for the new probabilities that\n",
"a shell hits the plane and the new probability that a surviving plane hits the target.\n",
"As a function of $\\gamma$ the probability of success is now\n",
"$$\n",
" {\\bf P}\\{\\hbox{success}\\}=\\sum_{n=1}^{16}\\big(1-(1-\\gamma p_D)^n\\big){20\\choose 16-n}\n",
" (\\gamma p_L)^{16-n}(1-\\gamma p_L)^{4+n}.\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "888f7386-d997-4438-af7b-603de6f6825c",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Psg (generic function with 1 method)"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# The probability P(TL=m) when gamma=g\n",
"PTLg(g,m)=binomial(20,m)*(g*pL)^m*(1-g*pL)^(20-m)\n",
"# Expected number of planes remaining with gamma=g and m planes\n",
"ESLg(g,m)=sum(n*PTLg(g,m-n) for n=1:m)\n",
"# The probability of success with gamma=g, pD=p and m planes\n",
"Psg(g,p,m)=sum((1-(1-g*p)^n)*PTLg(g,m-n) for n=1:m)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "7f776495-2328-494c-9c1c-e2a7419b7359",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
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\")
"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(g->Psg(g,0.7,16),0.05:0.01:1.0,title=\"Vary p with N fixed\",\n",
" ylabel=\"P(success)\",xlabel=\"gamma\",label=\"p=0.7 N=16\")\n",
"plot!(g->Psg(g,0.4,16),0.05:0.01:1.0,\n",
" ylabel=\"P(success)\",xlabel=\"gamma\",label=\"p=0.4 N=16\")\n",
"plot!(g->Psg(g,0.2,16),0.05:0.01:1.0,\n",
" ylabel=\"P(success)\",xlabel=\"gamma\",label=\"p=0.2 N=16\")\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "2f0b53eb-c668-418d-8e80-913859f44b42",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\")
"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(g->Psg(g,0.7,16),0.05:0.01:1.0,title=\"Fix p and vary N\",\n",
" ylabel=\"P(success)\",xlabel=\"gamma\",label=\"p=0.7 N=16\")\n",
"plot!(g->Psg(g,0.7,8),0.05:0.01:1.0,\n",
" ylabel=\"P(success)\",xlabel=\"gamma\",label=\"p=0.7 N=8\")\n",
"plot!(g->Psg(g,0.7,4),0.05:0.01:1.0,\n",
" ylabel=\"P(success)\",xlabel=\"gamma\",label=\"p=0.7 N=4\")\n"
]
},
{
"cell_type": "markdown",
"id": "c796630f-fbb6-4dcd-b8be-47ce6821df03",
"metadata": {},
"source": [
"In all cases the curves are increasing functions of $\\gamma$. This means\n",
"the probability of mission success ${\\bf P}\\{\\hbox{success}\\}$ decreases\n",
"as the weather gets worse. Therefore, bad weather is advantageous to the defender."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "c612c09b-af13-44e0-9fd5-dd1ca0f9d0f7",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.10",
"language": "julia",
"name": "julia-1.10"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
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