Question

Show that the function || in (−1,1) and zero elsewhere is a possible density
function and find the corresponding distribution function.

Answer 1

Answer:

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

f(x)=

⎩

⎪

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎪

⎧

3

x

2

−1<x<2

0otherwise

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).