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Chapter 5: Q. 11 (page 346)

f(x),a continuous probability function, is equal to 112and the function is restricted to 0≤x≤12. What is P(0<x<12)?

Short Answer

Expert verified

TheP(0<x<12)is1

Step by step solution

01

Given Information 

Given in the question that, the f(x)remains a continuous probability function. It is equal to 112and the function is restricted to 0≤x≤12.

We have to find what is P(6≤x≤8).

02

Concept Introduction 

Consider the data in the question; the continuous probability function is written as follows:

f(x)=112,    0≤x≤120,    otherwise

Here, Xfollows a uniform distribution.

Therefore, the area between (0<x<12)creates a rectangle with xaxis.

Then the base is base=(12−0)and height is height=112

03

Calculation

For continuous random variable X, P(c<x<d)=P(c≤x≤d).

The value of P(0<x<12)is:

P(0<x<12)=base×height

=(12−0)×112

=1212

=1

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