Chapter 8 Multiple Choice

Which of the following is true about f(x) when X has a uniform distribution over the interval [a, b]? a. The values of f(x) are different for various values of the random variable X. b. f(x) equals one for each possible value of X. c. f(x) equals one divided by the length of the interval from a to b. d. None of these choices.

c. f(x) equals one divided by the length

The probability density function, f(x), for any continuous random variable X, represents: a. all possible values that X will assume within some interval a x b. b. the probability that X takes on a specific value x. c. the height of the density function at x. d. None of these choices.

c. the height of the density function at x.

Suppose f(x) = 0.25. What range of possible values can X take on and still have the density function be legitimate? a. [0, 4] c. [2, +2] b. [4, 8] d. All of these choices are true.

d. All of these choices are true.

What is the shape of the probability density function for a uniform random variable on the interval [a, b]? a. A rectangle whose X values go from a to b. b. A straight line whose height is 1/(b a) over the range [a, b]. c. A continuous probability density function with the same value of f(x) from a to b. d. All of these choices are true.

d. All of these choices are true.

Which of the following is always true for all probability density functions of continuous random variables? a. The probability at any single point is zero. b. They contain an uncountable number of possible values. c. The total area under the density function f(x) equals 1. d. All of these choices are true.

d. All of these choices are true.

Which of the following represents a difference between continuous and discrete random variables? a. Continuous random variables assume an uncountable number of values, and discrete random variables do not. b. The probability for any individual value of a continuous random variable is zero, but for discrete random variables it is not. c. Probability for continuous random variables means finding the area under a curve, while for discrete random variables it means summing individual probabilities. d. All of these choices are true.

d. All of these choices are true.

The probability density function f(x) for a uniform random variable X defined over the interval [2, 10] is a. 0.20 c. 4 b. 8 d. None of these choices.

d. None of these choices.

The probability density function f(x) of a random variable X that has a uniform distribution between a and b is a. (b + a)/2 c. (a b)/2 b. 1/b 1/a d. None of these choices.

d. None of these choices.

If the random variable X has a uniform distribution between 40 and 50, then P(35 X 45) is: a. 1.0 c. 0.1 b. 0.5 d. undefined.

b. 0.5

Suppose f(x) = 1/4 over the range a x b, and suppose P(X > 4) = 1/2. What are the values for a and b? a. 0 and 4 b. 2 and 6 c. Can be any range of x values whose length (b a) equals 4. d. Cannot answer with the information given.

b. 2 and 6

Which of the following does not represent a continuous uniform random variable? a. f(x) = 1/2 for x between 1 and 1, inclusive. b. f(x) = 10 for x between 0 and 1/10, inclusive. c. f(x) = 1/3 for x = 4, 5, 6. d. None of these choices represents a continuous uniform random variable.

c. f(x) = 1/3 for x = 4, 5, 6.