STA301 Quiz Set 3

Q1. Marks = 10

Let X be a continuous random variable whose probability density function is:

For an interval 0<x<c. What is the value of constant c that makes f(x) a valid probability density function?

Solution:

x f x  0<x<c

For p.d.f 1. f x  x R

2. f x dx

First condition is satisfies because x is positive in the interval, So f(x) is also positive. Now according to 2nd condition c

c

c x dx

x

x

c

c

c c c So x to be a p.d.f function. x f x 

Spring-2022 · STA-301 Statistic and Probability Assignment No. 2 · Usman Mughal