Question 12. Let X, Y be two random variables and take values in {0,1} and whose joint distribution is given by: Joint Distribution Y = 0 Y=1 fx(x) X = 0 0.25 0.25 0.5 X = 1 0.25 0.25 0.5 fy(y) 0.5 0.5 1 Mark the choice that is FALSE: (a) E(X² + Y2) = E(X) + E(Y) (b) X and Y are statistically independent. (c) E(X²) = (E(X))² (d) var(X) = var(Y) (e) P(X = 1|Y = 1) = P(X = 1|Y = 0)

Please show step by step explanations. Thank you.

Question 8. This question is similar to Exercise 11 on page 363 of your textbook. Let t be a t-random variable. P(ta) = 0.05 and 65 degrees of freedom. Use Excel function =t.inv to find a. ii. Use Excel function =t.dist to find P(t 2.16) with df =23 This is a fill-in-blank question. Do not show your work. Write your answer with the format of #.###, #.####, #.####. The first number is for (i), the second number is for (ii), and so on.

Probability and Stats