hree balls are selected simultaneously and randomly from a box. But assume that the box contains 8 red balls and 5 green balls. Also assume that each red ball selected pays $0.30, that each green ball selected pays $0.70, and that it costs $1.30 to play the game. A random variable X is defined to be the net payoff for a player. How many different values are possible for the random variable X

An experiment consists of rolling a pair of fair dice, one red and one green. An outcome is an ordered pair (r,g), where r is the number on the red die and g is the number on the green die. List all outcomes of this experiment.

ANSWERS ALL PARTS A,B,C A) Roll a dice, X=the number obtained. Calculate E(X), Var(X). Use two expressions to calculate variance. B) Two fair dice are tossed, and the face on each die is observed. Y=sum of the numbers obtained in 2 rolls of a dice. Calculate E(Y), Var(Y). C) Roll the dice 3 times, Z=sum of the numbers obtained in 3 rolls of a dice. Calculate E(Z), Var(Z) from the result of part a and b.

There are 20 different pairs of shoes. Pick at random 10 shoes. Let X be the number of paired shoes, M be the number of shoes that are left-foot, N be the number of shoes that are right-foot.   (a)  Find the distribution of X. Show your problem-solving process (not just the final answer) with a few sentences of explanation and give the formula   (b)  Let Y = M – N. Give all possible values of Y. Find the distribution of Y. Show your problem-solving process (not just the final answer) with a few sentences of explanation and give the formula.   (c)  let Z = |Y|, compute E(X), Var(X), E(Z) and Var(Z). Show your problem-solving process (not just the answer), keep 2 decimal places for E(X) and E(Z), and use the approximate values for the calculations of Var(X) and Var(Z).