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3. (Independent Trials). A rifleman hits (H) his target with probability 9/13, and hence misses (M) with probability 4/13. He fires four times. (i) Write down all the elements of the event A that the man hits the target exactly twice (e.g. the samples MMHH and MHMH belong to A, but the samples HHHM and MMMH don't) and find P(A). (ii) Assuming independence of shots, find the probability that the man hits the target at least once. For Problem 4, apart from the main table showing the numerical answers to (sub)problems, for each random variable Z under consideration having the set of values {21, 2, ..., ze} and the distribution function f, provide a standard table showing the process of determination of the expected value E(Z) and the expected value E(Z?) of Z2: || 21 | Total Zk 2 ... f(zk) Zkf(Zk) f(22) f(21) 21f(z1) 2f(22) (zk) | zif(21) | 23f(2) f(ze) zef(ze) zef (ze) ... As is was discussed in class, whenever all entries in a given table are rational numbers, they can be entered, for convenience's sake, 'as they are'; otherwise, please round all the entries of the table to 5-digit floating-point numbers.

3. (Independent Trials). A rifleman hits (H) his target with probability 9/13, and hence misses (M) with probability 4/13. He fires four times. (i) Write down all the elements of the event A that the man hits the target exactly twice (e.g. the samples MMHH and MHMH belong to A, but the samples HHHM and MMMH don't) and find P(A). (ii) Assuming independence of shots, find the probability that the man hits the target at least once. For Problem 4, apart from the main table showing the numerical answers to (sub)problems, for each random variable Z under consideration having the set of values {21, 2, ..., ze} and the distribution function f, provide a standard table showing the process of determination of the expected value E(Z) and the expected value E(Z?) of Z2: || 21 | Total Zk 2 ... f(zk) Zkf(Zk) f(22) f(21) 21f(z1) 2f(22) (zk) | zif(21) | 23f(2) f(ze) zef(ze) zef (ze) ... As is was discussed in class, whenever all entries in a given table are rational numbers, they can be entered, for convenience's sake, 'as they are'; otherwise, please round all the entries of the table to 5-digit floating-point numbers.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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3. (Independent Trials). A rifleman hits (H) his target with probability 9/13, and hence misses (M) with probability 4/13. He fires four times. (i) Write down all the elements of the event A that the man hits the target exactly twice (e.g. the samples MMHH and MHMH belong to A, but the samples HHHM and MMMH don't) and find P(A). (ii) Assuming independence of shots, find the probability that the man hits the target at least once. For Problem 4, apart from the main table showing the numerical answers to (sub)problems, for each random variable Z under consideration having the set of values {21, z2, ..., ze} and the distribution function f, provide a standard table showing the process of determination of the expected value E(Z) and the expected value E(Z2) of Z2: Zk 21 22 Ze Total f(zk) Zkf(Zk) f(ze) Zef (ze) zef (ze) f(2) f(21) zif(21) 2f(z2) 了() |2f(21) |(22) As is was discussed in class, whenever all entries in a given table are rational numbers, they can be entered, for convenience's sake, 'as they are'; otherwise, please round all the entries of the table to 5-digit floating-point numbers.
Transcribed Image Text:3. (Independent Trials). A rifleman hits (H) his target with probability 9/13, and hence misses (M) with probability 4/13. He fires four times. (i) Write down all the elements of the event A that the man hits the target exactly twice (e.g. the samples MMHH and MHMH belong to A, but the samples HHHM and MMMH don't) and find P(A). (ii) Assuming independence of shots, find the probability that the man hits the target at least once. For Problem 4, apart from the main table showing the numerical answers to (sub)problems, for each random variable Z under consideration having the set of values {21, z2, ..., ze} and the distribution function f, provide a standard table showing the process of determination of the expected value E(Z) and the expected value E(Z2) of Z2: Zk 21 22 Ze Total f(zk) Zkf(Zk) f(ze) Zef (ze) zef (ze) f(2) f(21) zif(21) 2f(z2) 了() |2f(21) |(22) As is was discussed in class, whenever all entries in a given table are rational numbers, they can be entered, for convenience's sake, 'as they are'; otherwise, please round all the entries of the table to 5-digit floating-point numbers.
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