Question

Let random variable x be a continiuos random variable and it's p.d.f is given as f(x)=3x^2, 0<x<1 Find the probobility that random variable X exceeds the value of 1/2

Answer 1

Let random variable x be a continous random variable and it’s probabilty density function is given as;
f(x) = 3x2 , 0 < x < 1

To find : The probobility that random variable X exceeds the value of 1/2.

Now,

The area of the region for X>1/2 under X lies in (0, 1).

So

Therefore the probobility that random variable X exceeds the value of 1/2 is 0.875