HSC Arts 12th Board ExamMaharashtra State Board
Account
It's free!

User


Login
Create free account


      Forgot password?
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Solution - Given the P. D. F. (Probability Density Function) of a Continuous Random Variable X as - HSC Arts 12th Board Exam - Mathematics and Statistics

Question

Given the p. d. f. (probability density function) of a continuous random variable x as :

 `f(x)=x^2/3, -1`

         = 0 , otherwise

Determine the c. d. f. (cumulative distribution function) of x and hence find P(x < 1), P(x ≤ -2), P(x > 0), P(1 < x < 2)

Solution

c.d.f. of the continous random variable is given by

`F(x)=int_-1^xy^2/3dx`

`=[y^3/9]_-1^x`

`=(x^3+1)/9, x in R`

Consider P(X<1)=F(1)=(13+1)/9=2/9

`P(x<=-2)=0`

`P(X>0)=1-P(X<=0)`

`=1-F(0)`

`=1-(0/9+1/9)`

`=8/9`

`P(1<x<2)=F(2) - F(1)`

`=1-(1/9+1/9)`

=`7/9`

 

Is there an error in this question or solution?

APPEARS IN

 2014-2015 (March) (with solutions)
Question 6.2.3 | 4 marks
 2016-2017 (March) (with solutions)
Question 6.2.3 | 4 marks
Solution for question: Given the P. D. F. (Probability Density Function) of a Continuous Random Variable X as concept: null - Probability Density Function (P.D.F.). For the courses HSC Arts, HSC Science (General) , HSC Science (Electronics), HSC Science (Computer Science)
S