question 1

An number cube (a fair die) is rolled 3 times. For each roll, we are interested in whether the roll comes up even or odd. An outcome is represented by a string of the sort owe (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll). For each outcome, let /V be the random variable counting the number of even rolls in each outcome. For example, if the outcome is eoo, then N (eoo) = 1. Suppose that the random variable X is defined in terms of N as follows: X" = N-1. The values of X are given in the table below. Outcome ooo oeo eee ove vee eeo eve Value of X - 1 0 2 0 0 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 00 X 5 ? P(X=x) 0 0Let X be a random variable with the following probability distribution. Value x of X P(X=x) - 1 0.10 0.35 0.10 NJ 0.05 UJ 0.10 4 0.30 Complete the following. (If necessary, consult a list of formulas.)Complete the following. (If necessary, consult a list of formulas.) (a) Find the expectation E (X ) of X. E (X) = 1 X 5 ? (b) Find the variance Var(Y ) of X. var(X) = 0