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Which of the following is always true for all probability density functions of continuous random variables?...

Which of the following is always true for all probability density functions of continuous random variables?

A. They have the same height

B. They are bell-shaped

C. They are symmetrical

D. The area under the curve is 1.0

Like the normal distribution, the exponential density function f(x)

A. is bell-shaped

B. approaches zero as x approaches infinity

C. approaches infinity as x approaches zero

D. is symmetrical

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

1.

options A,B,C are properties which are not necessarily found in all probability density functions

sum of all probabilities = 1

area under curve in probability density of continuous random variable is the sum of all probabilities

therefore area under the curve is 1.0

answer = D. The area under the curve is 1.0

2.

expnential density function curve

Normal distribution curve

we can see only thing that is common is : both approaches zero as x approaches infinity

answer : B. approaches zero as x approaches infinity

P.S. (please upvote if you find the answer satisfactory)

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