00:01
In this question, in the a part, the likelihood function l is equal to product i is equal to 1 to n f x xi comma theta, which is equal to product i is equal to 1 to n 3x2 over theta cube.
00:21
Now l is equal to 3 raise to par n over theta cube n product i is equal to 1 to 0.
00:30
X i square x i square now taking the log both sides we got log l is equal to n log 3 plus log product x i square minus 3x log theta 3 n log theta which is equal to n log 3 plus submission log x i square plus submission log x i square minus 3 n log theta now here to find the m -l -e, we have to maximize l at theta, which is xn.
01:08
Now m -l -e, theta to xn is equal to maximum x1, x2, up to xn.
01:17
So now in the b part, e xn is equal to integration, exn is equal to integration 0 to theta x, fxn, dx.
01:27
Now f x is equal to integration 0 to x 3 t scale over theta cube d t which is equal to x cube over theta cube which is equal to n x cube over theta cube raised to par n minus 1 3x scale divide by theta cube now this is equal to f x n which is equal to 3 n x x raise to par 3n minus 3 plus 2 divide by theta raised to par 3n minus 3 plus 3.
02:07
Now fxn is equal to 3n x raised to par 3n minus 1 divide by theta 3n.
02:16
Theta raised to 3n...