11- Consider the sample space S= {(-2, 4), (-1, 1), (0, 0), (1, 1), (2,4)},where each point is assumed to be equally likely. Define the randomvariable X to be the first component of a sample point and Y, the second.Then, the cov (X, Y) is(a) 2OabO Cсd(b) -2(c) 0(d) 1

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Answered: 11- Consider the sample space S= {(-2,…

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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Let X and Y be any two random variables and let a and b be any two real numbers. Then var(ax + bY) = a² var(X) + b?var(Y) + 2ab cov(X,Y). False True
3) A random variable X takes the values 0, 2 and 3 with probabilities 0.3, 0.1 and 0.6, respectively. A random variable in the form of Y = 3(X-1)2 is defined. a) Find the expected value and variance of the random variable X. b) Find the variance of the Y random variable. c) Find the cumulative distribution function of the Y random variable.
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An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of heads in each outcome. For example, if the outcome is hhh, then N (hhh) = = 3. Suppose that the random variable X is defined in terms of N as follows: X=6N-2N²-3. The values of X are given in the table below. Outcome hhh hth hht thh htt tth ttt tht Value of X-3 1 1 1 1 1 -3 1 Calculate the probabilities P (X=x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value X of X P(X=x) 0 0 0 00 X
In experiment of flipping two coins, each coin has two faces: Head and Tail. Each face is being equally likely to be drawn. If two random variables X and Y are defined as X(s) = Number of Heads appeared on both coins Y(s) = Number of Tails appeared on both coins The value of pxy (2,0) is 00.5 00 01 00.25
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (*) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of heads in each outcome. For example, if the outcome is ttt, then N (ttt) = 0. Suppose that the random variable X is defined in terms of N as follows: X=2N -2. The values of X are given in the table below. Outcome ttt hth tht htt thh hhh hht tth Value of X -2 2 0 0 2 4 2 0 Calculate the probabilities P(X=*) of the probability distribution of X. First, fill in the first row with the valuesof X. Then fill in the appropriate probabilities in the second row. Value x of X ___ ___ ___ ___ P(x=x) ___ ___ ___ ___
Let X(1), X(2), ..., X(n) be the order statistics of a set of n independent uniform (0, 1) random variables.Find the conditional distribution of X(n) given that X(1) = s(1), X(2) = s(2), ..., X(n-1)=s(n-1).
Let X and Y be two random variables such that Cov(X.Y) = -3 . Then %3D O None of these O cov(-3X+5,-3Y+5)=-18 cov(3X+5,-2Y+5)=18 O cov(5X+3,-2Y-2)=-20
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of tails in each outcome. For example, if the outcome is hth, then N (hth) = 1. Suppose that the random variable X is defined in terms of N as follows: X=2N² − 6N-1. The values of X are given in the table below. Outcome thh tth hhh hth ttt htt hht tht Value of X-5 -5 -1 -5 -1 -5 -5 -5 Calculate the probabilities P(X=x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value X of X P(X=x) 0 0 00 X

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11- Consider the sample space S= {(-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4)}, where each point is assumed to be equally likely. Define the random variable X to be the first component of a sample point and Y, the second. Then, the cov(X, Y) is (a) 2 O a b (b) -2 (c) 0 (d) 1