Math Help - Consider a random sample of size n

1. Consider a random sample of size n

Question :

Consider a random sample of size $n$ from a population with the 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} \qquad for \ x = 0,1
$

2. Originally Posted by zorro
Question :

Consider a random sample of size $n$ from a population with the 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} \qquad for \ x = 0,1
$
Find the value of p that maximises L = f(0, p) f(1, p).

If you need more help, please show all of your working and state specifically where you're still stuck.

3. This is getting tiresome.
You posted 20 homework problems,
you don't make any effort
and on top of that you never thank anyone.
I'd ban this behaviour way before I'd ban someone from asking a question in the chatroom.

4. Is this correct?

Originally Posted by mr fantastic
Find the value of p that maximises L = f(0, p) f(1, p).

If you need more help, please show all of your working and state specifically where you're still stuck.

here is what i have done

$L(p)$ = $p^x (1 - p)^{1 - x}$

Taking log on both sides

$ln[L(p)]$ = $x \ ln(p) + (1 - x) \ ln(1 - p)$

Differentiating on both sides wrt p weget

$\frac{d}{dp} \ ln[L(p)]$ = $\frac{x}{p} + \frac{1 - x}{1 - p}$

Is it correct or have i done some thing wrong now what should i do further...

5. Originally Posted by zorro
here is what i have done

$L(p)$ = $p^x (1 - p)^{1 - x}$

Taking log on both sides

$ln[L(p)]$ = $x \ ln(p) + (1 - x) \ ln(1 - p)$

Differentiating on both sides wrt p weget

$\frac{d}{dp} \ ln[L(p)]$ = $\frac{x}{p} + \frac{1 - x}{1 - p}$

Is it correct or have i done some thing wrong now what should i do further...
My understanding from post #1 is that $L = f(0, p) \cdot f(1, p) = (1-p)p$. This has an obvious maximum.

However .... if the random sample is of size n then it's not clear to me what the n sample values of x are ....

My understanding from post #1 is that $L = f(0, p) \cdot f(1, p) = (1-p)p$. This has an obvious maximum.