The probability density function f(x) of a random variable X that is uniformly distributed between a and b is:
A)1/(b - a).
B)1/(a - b).
C)(b - a)/2.
D)(a - b)/2.

Question

Quizplus · Accepted Answer

The probability density function of a continuous uniform distribution is a constant k between the limits a and b, and zero elsewhere. To find k, we use the fact that the total area under the PDF must be equal to 1 (since the probability of X being between a and b is 1). Therefore, k times the width of the interval (b-a) must be equal to 1. Solving for k, we get k = 1/(b-a), which is choice A.

The Probability Density Function F(x) of a Random Variable X