Bayesian estimation of Expectation in Bernoulli problem
- From: quebecstat@xxxxxxx
- Date: Thu, 23 Aug 2007 07:49:52 -0700
Hi everyone,
I would be interested in a hint, a pointer or some help with the
following problem.
Consider two coins, C1 and C2, with the following characteristics:
Pr(heads| C1) = 0.6 and Pr(heads| C2) = 0.4.
Choose one of the coins at random and imagine spinning it repeatedly.
Given that the first two spins from the chosen coin are tails, what is
the expectation of the number of additional spins until a head shows
up?
Below I have indicated my work so far.
Many thanks
Let N be the number of additional spins until a head shows up
We have N|Pr(heads)=Geometric(Pr(heads))
and E{N|Pr(heads)}=1/Pr(heads)
E{N}=E[E{N|Pr(heads)}]=E[1/Pr(heads)]
Now I need to find Pr(heads)
That is where I am stuck. I do not know how to write the fact that the
coin is chosen at random.
What I have is
Pr(heads|first 2 spins are tails, C1)= ( (1-p)^2 *0.6 ) /((1-p)^2
*0.6+(1-p)^2 *.4)
Thanks for your help.
.
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