Can you do question 1 please?

I-Getxll-lel FonxIGExeXIGExeXIGExexl-I-HorxlMlnbrxl@'RexlNlelHorX Horx 6 9 0' Filel /Users/jefyhefy/Desktop/NYU/Homework4_for_Statistics%20(1).pdf Homework4_for_Statistics (1 ).pdf 123% + m [30 total points] 1. Suppose that a random variable X has a discrete distribution for which the p.f. is as follows: cm for w = 1,2, 3,4, 5,6, f (av) = . 0 otherw15e. Determine all the medians of this distribution. [2 points] . Suppose that 20 percent of the students who took a certain test were from school A and that the arithmetic average of their scores on the test was 80. Suppose also that 30 percent of the students were from school B and that the arithmetic average of their scores was 76. Suppose, nally, that the other 50 percent of the students were from school C and that the arithmetic average of their scores was 84. If a student is selected at random from the entire group that took the test, what is the expected value of her score? [2 points] . Suppose that X and Y are random variables for which E(X) = 3, E(Y) = 1, Va'r(X) = 4, and Var(Y) = 9. Let Z = 5X Y + 15. Find E(Z) and Var(Z) under each of the following conditions: (a) X and Y are independent; (b) X and Y are uncorrelated; (c) the correlation of X and Y is 0.25. [2 points] . Three men A, B, and C shoot at a target. Suppose that A shoots three times and the probability that he will hit the target on any given shot is 1/8, B shoots ve times and the probability that he will hit the target on any given shot is 1/4, and C shoots twice and the probability that he will hit the target on any given shot is 1 / 2. What is the expected number of times that the target will be hit? If we assume that all shots at the target are independent what is the variance of the number of times that the target will be hit?[2 points] SSupxluCotxl + QGElI-EJOE