Let ( X ) be normally distributed with mean ( mu ) and variance ( sigma^{2} ), where both ( mu ) and ( sigma^{2} ) are unknown. The likelihood function for a random sample of size ( n ) is ? Find for mean and variance.

The function shown in the figure.

Use Method of Maximum Likelihood

Example 4: Let X be normally distributed with mean and variance 02, where both and 2 are unknown. The likelihood function for a random sample of size n is 1 L(H, )=2 i=1 e(x)/(20) = 1 (22)/2 e(1/20),(x,)