Consider a random sample n from a population

[TomJerry]

Problem: Consider a random sample n from a population with probability distribution f(x,p) that depends on parameter p. Find the maximum likelihood estimator for p when

f(x,p) = p^x (1-p)^1-x for x=0,1

 

[statdad]

So you've tried...?

 

[TomJerry]

So you've tried...?

I m having difficulty starting , can you show me an example which is near to this or related to this . I just need a starting point .

 

[statdad]

The likelihood function is

$$L(p \colon x_1, x_2, \dots, x_n) = \prod_{i=1}^n p^{x_i} (1-p)^{1-x_i}$$

Break the product into two factors, one in which $$x_j = 0$$, the other in which $$x_j = 1$$, and see what the products look like.