00:01
In this question, given probability density function, that is f of x equal to k into 1 minus x raise to minus 3, 1 less than x less than 2, we have to find the variance.
00:16
So, first we have to find the k, that is, integral f of x dx equal to 1.
00:24
So, integral 1 to 2, k into 1 minus x raise to minus 3, dx is equal to 1.
00:36
So integrate this, we get k into x minus x raised to minus 2 by minus 2, integral 1 to 2 which is equal to 1.
00:50
So after solving this, we get k is 8 by 5.
00:57
The equation for finding variance is variance of x is expectation of x square minus expectation of x the whole square.
01:12
So expectation of x square is calculating using the equation integral 1 to 2 x square into f of x d x.
01:21
Our f of x is 8 by 5 into 1 minus x raised to minus 3 d x...