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

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 .

Quizplus · Accepted Answer

The probability density function of a uniform distribution is a constant value over the interval [a,b]. Since the total area under the probability density function must be equal to 1, we have:

∫f(x)dx = 1

Since the probability density function is constant over the interval [a,b], we can write:

∫f(x)dx = f(x)∫dx = f(x)(b-a)

Therefore,

f(x)(b-a) = 1

Solving for f(x), we get:

f(x) = 1 / (b-a)

So, the correct answer is A, which is 1/(b-a).

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