stat chp 8

A probability density function shows the probability for each value of X. (T/F)

F

Continuous probability distributions describe probabilities associated with random variables that are able to assume any finite number of values along an interval. (T/F)

F

The sum of all values of f(x) over the range of [a, b] must equal one. (T/F)

F

A continuous random variable X has a uniform distribution between 10 and 20 (inclusive), then the probability that X falls between 12 and 15 is 0.30. (T/F)

T

Since there is an infinite number of values a continuous random variable can assume, the probability of each individual value is virtually 0. (t/f)

T

To be a legitimate probability density function, all possible values of f(x) must be non-negative. (T/F)

T

Suppose X is a continuous random variable for X between a and b. Then its probability ____________________ function must non-negative for all values of X between a and b.

density

The probability density function, f(x), for any continuous random variable X, represents:

the height of the density function at x

The probability density function of a uniform random variable on the interval [0, 5] must be ____________________ for 0 x 5.

1/5

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

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 them

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

You can use a continuous random variable to ____________________ a discrete random variable that takes on a countable, but very large, number of possible values.

approximate

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.

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 of the interval from a to b.