Question

(This is a multiple choice question, so the answer is either A, B, C, or D.)

Question: For probability density function of a random variable X, P(X < a) can also be described as:

A.) The area under the curve to the right of a.

B.) F(a), where F(X) is the cumulative distribution function.

C.) The area under the curve between 0 and a.

D.) 1- F(a) where F(X) is the cumulative distribution function.

Answer 1

Let , f(x) be the probability density function of a random variable X.

Since , the random variable is continuous random variable.

The cumulative distribution function of X is ,

Correct answer is (B) F(a) , Where F(x) is the cumulative distribution function.

A) The area under the curve to the right of a.

The statement is false. Because it is the area under the curve to the left of a.

i.e.

B) F(a) , Where F(x) is the cumulative distribution function.

The statement is true. Because by definition of cumulative distribution function ,

C) The area under the curve between 0 and a.

The statement is false. Because for the cumulative distribution function ,

D)  1- F(a) where F(X) is the cumulative distribution function.

The statement is false. Because