Chapter 8, Problem 21RE

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

Chapter
Section

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

# (a) Explain why the function f ( x ) = { π 20 sin ( π x 10 ) if 0 ≤ x ≤ 10 0 if x < 0   or  x > 10 is a probability density function. (b) Find P(X < 4). (c) Calculate the mean. Is the value what you would expect?

(a)

To determine

To explain: the given function as probability density function with explanation.

Explanation

Given information:

The given function is f(x)=Ï€20sin(Ï€x10) , if 0â‰¤xâ‰¤10 and f(x)=0 if x<0 or x>10

Calculation:

Show the function as follows:

f(x)=Ï€20sin(Ï€x10) (1)

Show the conditions of probability density function as follows:

(A) The probability density function f of a random variable X satisfies the condition f(x)â‰¥0 for all x.

(B) The probabilities are measured on a scale from 0 to 1, it follows that âˆ«âˆ’âˆžâˆžf(x)â€‰dx=1 .

Apply the probability density function (B) in Equation (1) as shown below

(b)

To determine

To calculate: The value of P(X<4) .

(c)

To determine

To calculate: The value of mean

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