Which of the following is true about f(x)when X has a uniform distribution over the interval [a,b]?
A)The values of f(x)are different for various values of the random variable X.
B) f(x)equals one for each possible value of X.
C)F(x)equals one divided by the length of the interval from a to b.
D) None of these choices.

Question

Quizplus · Accepted Answer

When X has a uniform distribution over the interval [a,b], the probability of X being any value within the interval is equal. Therefore, the probability density function (PDF) f(x) must be constant within the interval. We can find this constant by recognizing that the area under the PDF curve must integrate to 1 over the interval. Therefore, the height of the PDF curve must be such that the area under it is equal to 1, which is achieved by dividing 1 by the length of the interval from a to b. So, f(x) equals one divided by the length of the interval from a to b.

Which of the Following Is True About F(x)when X Has