00:01
Hello students here we are given x follows exponential distribution with the parameter 87.
00:09
So f of x is equal to 87 e power minus 87 x if x is greater than 0.
00:21
So first question y is equal to e power minus x expectation of y is equal to expectation of e power minus x which is equal to 0 to infinity e power minus x f of x into dx which is equal to 0 to infinity e power minus x 87 e power minus 87 x into dx.
00:47
So this is equal to 0 to infinity 87 into e power minus 87 x into dx which is 87 into e power minus 88 x divided by 88 0 to infinity.
01:23
So this is equal to 87 by 88 which is equal to 0 .9886.
01:37
Then the second question b so variance of y is equal to expectation of y square minus expectation of y whole square.
01:58
So this is equal to expectation of y square is equal to expectation of e power minus 2x which is equal to 0 to infinity e power minus 2x into 87 e power minus 87 into x into dx.
02:18
This is equal to 87 0 to infinity e power minus 89 x into dx.
02:30
So this is equal to 87 by 89 minus e power minus 89 x into 0 to infinity.
02:41
So this is equal to 87 by 89.
02:48
So variance of y is equal to 87 by 89 minus 87 by 88 whole square.
02:58
So this is equal to 0 .00012623...