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 {z1, 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(Z?) of Z2: 21 || Total 22 ... ze f (z2) f (zk) Zkf(zk) 21f(21) 22f(z2) zf(zk) || 2if(z1)| 23f(22) f(ze) ze f (ze) zef(ze) f(21) ... ... ... 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. 4. (Random Variables). (i) A coin weighted so that P(H) = 20/37 and P(T) = 17/37 is tossed four times. Let X be the random variable which denotes the length of the longest string of heads which occurs. Find the distribution, expectation, variance and standard deviation of X. (ii) A fair coin is tossed until a head or 7 tails occur. Let X be the random variable which denotes the number of tosses. Find the distribution, expectation, variance and standard deviation of X. (iii) A player tosses three fair four-faced dice. If the sum is prime, he wins that number of dollars, but otherwise he loses that number of dollars. Find the expected value of the game, and determine which of the following is true: (a) the game is favorable for the player, (b) the game is unfavorable for the player, (c) the game is fair.
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 {z1, 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(Z?) of Z2: 21 || Total 22 ... ze f (z2) f (zk) Zkf(zk) 21f(21) 22f(z2) zf(zk) || 2if(z1)| 23f(22) f(ze) ze f (ze) zef(ze) f(21) ... ... ... 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. 4. (Random Variables). (i) A coin weighted so that P(H) = 20/37 and P(T) = 17/37 is tossed four times. Let X be the random variable which denotes the length of the longest string of heads which occurs. Find the distribution, expectation, variance and standard deviation of X. (ii) A fair coin is tossed until a head or 7 tails occur. Let X be the random variable which denotes the number of tosses. Find the distribution, expectation, variance and standard deviation of X. (iii) A player tosses three fair four-faced dice. If the sum is prime, he wins that number of dollars, but otherwise he loses that number of dollars. Find the expected value of the game, and determine which of the following is true: (a) the game is favorable for the player, (b) the game is unfavorable for the player, (c) the game is fair.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text: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 {z1, 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(Z?) of Z2:
Zk
z1
22
ze
Total
..
f(z1)
f(zk)
Zk f(zk) || 21f(z1) | 2f(2)
zf(zk) || z²f(z1)| 23f(22)
f(ze)
ze f (ze)
... zef(ze)
f(z2)
..
...
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.
4. (Random Variables). (i) A coin weighted so that P(H) = 20/37 and P(T) = 17/37 is tossed four times. Let X be the random
variable which denotes the length of the longest string of heads which occurs. Find the distribution, expectation, variance and standard
deviation of X.
(ii) A fair coin is tossed until a head or 7 tails occur. Let X be the random variable which denotes the number of tosses. Find the
distribution, expectation, variance and standard deviation of X.
(iii) A player tosses three fair four-faced dice. If the sum is prime, he wins that number of dollars, but otherwise he loses that
number of dollars. Find the expected value of the game, and determine which of the following is true: (a) the game is favorable for
the player, (b) the game is unfavorable for the player, (c) the game is fair.
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