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

Quote by statdad

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

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

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

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TomJerry	Consider a random sample n from a population 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 Recognitions: Homework Help	Consider a random sample n from a population The likelihood function is [tex] L(p \colon x_1, x_2, \dots, x_n) = \prod_{i=1}^n p^{x_i} (1-p)^{1-x_i} [/tex] Break the product into two factors, one in which [tex] x_j = 0 [/tex], the other in which [tex] x_j = 1 [/tex], and see what the products look like.