Question

***Solve without derivative and please explain all the steps in your work. Thanks.

4. Uniform Distributions. A random number generator randomly selects a number from -2 to 1.

It is equally likely to select any number from this interval [-2,1]. We can view this random

variable as a continuous random variable.

(a)

What is the constant height required to ensure that the area between the x axis and the

curve is exactly one in this case (note since this is a uniform distribution the density curve is

a horizontal line)?

(b)

What is the probability that a randomly generated number is less than -1?

(c)

What is the probability that a randomly generated number is greater than -1?

(d)

What is the probability that a randomly generated number is greater than 0.5?

(e)

What is the probability that a randomly generated number is either greater than 0.5 or less

than -1?

(f)

What is the probability that a randomly generated number is 0.5?

Answer 1