HSC Science (Computer Science) 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 for Given the P. D. F. (Probability Density Function) of a Continuous Random Variable X as - HSC Science (Computer Science) 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: Probability Distribution - Probability Density Function (P.D.F.). For the courses HSC Science (Computer Science), HSC Arts, HSC Science (Electronics), HSC Science (General)
S