week 9 carmen quiz: continuous random variables

Which of the following is NOT a continuous random variable?

-All of the choices are continuous random variables -Length of time between accidents at an intersection -Number of accidents in one year at an intersection = ANSWER -Time waiting on the phone for tech support (in seconds)

Suppose X is a continuous random variable with the pdf defined as below: f(x) = 1/9(x^2), 0 < x < 3. What is the probability that x is greater than 2?

.7

Let f(x) = 3x^2for 0 < x < 1. What is the median of X? Choose the closest answer!

.8

Suppose X is a continuous random variable with the pdf defined as below: f(x) = 1/9(x^2), 0 < x < 3. What is P(X=2)?

0

Suppose X has a uniform distribution on the interval [0, 10]. What is f(x)?

1/10

Let f(x) = kx where x is between 0 and 2. What is the value of k that makes this a legitimate density function?

1/2

f(x) = 1/2 between 0 and 2. What is the probability that X is between 1 and 3?

1/2

Let f(x) = 3x^2 for 0 < x < 1. What is P(X < 1/2)? Choose the closest answer!

1/8

Suppose X is a continuous random variable with the pdf defined as below: f(x) = 1/9(x^2), 0 < x < 3. What is the mean of X?

2.25

Let f(x) = 3x^2 for 0 < x < 1. What is the mean of X? Choose the closest answer!

3/4

Suppose X is a continuous random variable with the pdf defined as below: f(x) = 1/9(x^2), 0 < x < 3. What is f(2)?

4/9

Suppose X is a continuous random variable with the pdf defined as below: f(x) = 1/9(x^2), 0 < x < 3. True or false? The median of X is 1.5.

false

Suppose f(x) = 1/2 where 0 < X < 2. True or false? The median of X is 0.50.

false

True or false? Let X be a continuous random variable. Then f(x) must always lie between 0 and 1.

false

True or false? When you integrate e^(-x), you get e^(-x).

false

A probability density function f(x) tells you how much probability is in the area near x.

true

Let f(x) = 3x^2 for 0 < x < 1. True or False? P(X < 1/2) = P(X <= 1/2)

true

Suppose X has a uniform distribution on the interval [0, 10]. True or false, the mean of X is 5.

true

With a continuous random variable, P(a < X < b) is the area under the curve f(x) between a and b.

true

A continuous random variable has a(n) __________________________ number of possible values.

uncountably infinite