Question

The probability distribution of random variable X is given below. What is E[X]?

X	4	2	6
P(x)	0.6	0.2	0.2

The probability distribution of random variable X is given below. What is σ²_x?

X	4	2	6
P(x)	0.6	0.2	0.2

The probability distribution of random variable X is given below. Let Y = 4X − 5 be a new random variable. What is σ²_y?

X	4	2	6
P(x)	0.6	0.2	0.2

The probability distribution of random variable X is given below. Let W = X² − X be a new random variable. What is σ²_w?

X	4	2	6
P(x)	0.6	0.2	0.2

The probability distribution of random variable X is given below. What is E[X]?

X	1	2
P(x)	0.6	0.4

The probability distribution of random variable X is given below. Let Y = 3X² − 1 be a new random variable. What is σ_y?

X	1	2
P(x)	0.2	0.8

In basketball, free throws are unopposed attempts to score points from a fixed distance away from the basket and are awarded to a player when the opposite team breaks particular rules. “Converting” a freethrow means that the ball goes through the basket and a point is successfully scored. A player shoots either two free-throws consecutively, or shoots what’s called a “one-and-one,” in which a second free-throw attempt is allowed only if the first attempt was successful. Assume that a player’s free-throw attempts are independent. Lakshmi converts 75% of her free-throws. She is awarded two consequtive free-throws. The random variable X is the number of points resulting from Lakshmi’s two free-throw attempts. What is E[X]?

Linh converts 65% of their free throws. They get to shoot a “one and one.” The random variable W is the number of points resulting from Linh’s “one-and-one” attempt. What is E[W]?

The Cubs team will play 5 baseball games against the Cardinals team. For any one game it is estimated that the probability of a Cubs win is 0.55, and the outcomes of the 5 games are independent. Let X be the number of games that the Cubs win in the series. What is σ_X?

The Cubs team will play 5 baseball games against the Cardinals team. For any one game it is estimated that the probability of a Cubs win is 0.4, and the outcomes of the 5 games are independent. Let X be the number of games that the Cubs win in the series. What is the probability that the Cubs win a majority of the games in the series?

Answer 1