00:01
Hello everyone, let us look into the equation.
00:04
So, to find the cumulative distribution function of y, we need to compute p of y less than or equal to y for y greater than or equal to 0.
00:14
Now, consider p of y less than or equal to y which is equal to p of x square by 2 less than or equal to y.
00:22
So, which means that p of x less than or equal to square root of 2 y.
00:27
So, hence we can have f x of x equal to 3 x square by 8.
00:33
So, now p of y less than or equal to y equal to integral square root of 2 y 3 x square by 8 dx.
00:45
So, upon simplification we may get it as 5 power 3 by 2 divided by 4, this is the value of p of y less than or equal to y.
00:54
Similarly, we have to find the cumulative distribution function of y f y of sorry the cumulative distribution function of y f y of y is p of y less than or equal to y which is y power 3 by 2 divided by 4 for y greater than 0.
01:14
Now, from this we can have e of y equal to integral 0 to infinity f y of y dy which is equal to integral 0 to infinity 3 by 4 times 2 y power minus 1 by 2 dy which is equal to 3 by 2 times integral 0 to infinity u square du where we are taking u equal to square root of 2 y.
01:45
So, which is equal to 3 by 2 times u cube by 3 from 0 to infinity which is infinity.
01:51
Next consider variance of y which is e of y square minus e of y the whole square...