The probability density function f(x) for a uniform random variable X defined over the interval [1, 11] is:
A) any value between 1 and 11 .
B) $0.100 .$
C) $0.091 .$
D) above $11 .$

Question

The probability density function f(x) for a uniform random variable X defined over the interval [1, 11] is: 
A) any value between 1 and 11 .
B) $0.100 .$
C) $0.091 .$
D) above $11 .$

Quizplus · Accepted Answer

For a uniform random variable, the probability density function is given by f(x)=$\frac{1}{b-a}$ where a and b are the lower and upper bounds of the interval. Therefore, for X defined over [1, 11], f(x)=$\frac{1}{11-1}$=$\frac{1}{10}$=0.1. Therefore, the correct choice is B, which corresponds to 0.1 as the probability density function for X.

The Probability Density Function F(x) for a Uniform Random Variable 0.100.0.100 .0.100.

The Probability Density Function F(x) for a Uniform Random Variable $0.100 .$