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In a soccer game, let the number of goals scored by the home team be denoted by the random variable X, and the number scored by the visiting team be denoted by the random variable Y. The probability distributions of X and Y are given below: x 0 1 2 P(X = x) 0.20 0.40 0.40 y 0 1 2 P(Y = y) 0.20 0.70 0.10 Assume that X and Y are independent random variables. Let T be the total number of goals scored in the game. 1. Which one of the following statements is true? A) The mean of a random variable is always positive. B) The variance of a random variable is always greater than the mean of that random variable. C) The variance of a random variable is always less than the mean of that random variable. D) None of these is true. E) The variance of a random variable can be negative. 2. What are the possible values that T can take ? A) None of these B) {0,1,2} C) {0,2,4} D) {0,1,2,3,4} E) {1,2,3} 3. Which one of the following is the probability that T = 3? A) 0 B) 0.38 C) None of these D) 0.32 E) 0.40

In a soccer game, let the number of goals scored by the home team be denoted by the random variable X, and the number scored by the visiting team be denoted by the random variable Y.
The probability distributions of X and Y are given below:

x 0 1 2
P(X = x) 0.20 0.40 0.40

y 0 1 2
P(Y = y) 0.20 0.70 0.10

Assume that X and Y are independent random variables. Let T be the total number of goals scored in the game.

1.
Which one of the following statements is true?
A) The mean of a random variable is always positive.
B) The variance of a random variable is always greater than the mean of that random variable.
C) The variance of a random variable is always less than the mean of that random variable.
D) None of these is true.
E) The variance of a random variable can be negative.
2.
What are the possible values that T can take ?
A) None of these
B) {0,1,2}
C) {0,2,4}
D) {0,1,2,3,4}
E) {1,2,3}
3.
Which one of the following is the probability that T = 3?
A) 0
B) 0.38
C) None of these
D) 0.32
E) 0.40

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