A discrete random variable X has the following probability distribution: Value of X 1 2 3 4 5 6 Probability 0.30 0.20 0.15 0.15 0.10 0.10 Find the probability that X is a multiple of 2. A) 0.10 B) 0.25 C) 0.45 D) 0.35 Find the probability X is greater than 1, or P(X > 1). A) 0.30 B) 0.50 C) 0.90 D) 0.70 Find the mean of the random variable X, μX. A) 4.15 B) 2.85 C) 3 D) 3.50

A random variable Y is given with its probability distribution. Find the value of 100q. 1 3 3q q Y P(Y) 0 0.35 2 0.25 4 9

X 1 2 3. A physics professor wants to know what percent of physics majors will spend the next several years doing post-graduate research. He has the following probability distribution. 3 4 5 6 P(x) 0.35 0.20 0.15 0.10 0.05 x*P(x a. Define the random variable x. b. Define P(x), or the probability of x. c. Find the probability that a physics major will do post-graduate research for four years. P(x = 4) =_ d. Find the probability that a physics major will do post-graduate research for at most three years. P(x ≤ 3) =_ e. On average, how many years would you expect a physics major to spend doing post-graduate research?

Let discrete random variables X and Y have the following probability distribution: Y 1 -1 0.10 0.18 0.10 X 0.09 0.15 0.23 1 0.03 0.05 0.07 Find the E(X2 Y²) -0.91 1.18 0.91 1.0494