00:02
Hi, here it is given in the first problem that we have in random samples x1 x2 xn which follows the distribution each follows distribution with the pdf fx theta.
00:20
Theta is our parameter of interest.
00:22
We'll find the amelia theta, maximum likelihood estimator of theta.
00:27
So for that we first find the likelihood function.
00:32
Now, it is given that first problem fx theta, the probative density function is theta x to the power theta minus 1, 0 less than x, less than 1, and theta greater than 0, and 0 otherwise.
00:56
Now, the likelihood function of theta given x curl, we denoted by l theta -colon -x curl, that is product of irons from 1 to n f x i.
01:12
So we'll get it theta to the word n product of irons from 1 to n x i i whole to the power theta minus 1.
01:25
Now we find the value of theta such that this likelihood function l theta is maximum.
01:35
Now maximizing this likelihood function, is equivalent to maximizing log likelihood function because log function is the increasing function of x, log x is the increasing function of x...