Let ZaXbY where X and Y are two discrete random variables while a and b are two

Let zaxby where x and y are two discrete random

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Let Z=aX+bY where X and Y are two discrete random variables while a and b are two constants. Using the formula for the expected value of a function of two discrete random variables (found on your cheat sheet), show that the variance of Z can be written as follows: Var(Z)=a 2 Var(X)+ b 2 Var(Y)+2abCov(X,Y) (10 points)
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Question 4 According to a recent report, 9.5% of Canadian students study abroad. Assume that 60% of Canadian students studying abroad are women and that 49% of Canadian students who do not study abroad are women. a) What is the probability that a female Canadian student is studying abroad? (6 points) b) What is the probability that a male Canadian student is studying abroad? (6 points) c) Imagine that we randomly chose 5 Canadian students. What is the probability of having three men? (8 points)
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Question 5 The following table presents the joint probability distribution of two discrete random variables X and Y. X 1 2 3 0 0.10 0.21 0.06 Y 1 0.05 0.10 0.11 2 0.02 0.11 0.24 a) Graph the conditional probability distribution of X given Y = 2 as a function of x. (6 points) b) Graph the cumulative probability function of Y as a function of y. (6 points)
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c) Calculate the correlation coefficient between X and Y. (10 points)
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Bonus : Using the definition of the expectation of a discrete random variable, show that the variance of a binomial distribution is np(1-p). (5 points)
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