s*******i
发帖数: 546 | 1 Consider the following process. We have two coins, one of which is fair, and
the
other of which has heads on both sides. We give these two coins to our
friend,
who chooses one of them at random (each with probability 1/2). During the
rest of the process, she uses only the coin that she chose. She now proceeds
to toss the coin many times, reporting the results. We consider this process
to consist solely of what she reports to us.
(a) Given that she reports a head on the nth toss, what is the prob | T*******t
发帖数: 9274 | 2 作业题？interview考这个就太无聊了
and
proceeds
process
【在 s*******i 的大作中提到】
: Consider the following process. We have two coins, one of which is fair, and
: the
: other of which has heads on both sides. We give these two coins to our
: friend,
: who chooses one of them at random (each with probability 1/2). During the
: rest of the process, she uses only the coin that she chose. She now proceeds
: to toss the coin many times, reporting the results. We consider this process
: to consist solely of what she reports to us.
: (a) Given that she reports a head on the nth toss, what is the prob
| s*******i
发帖数: 546 | 3 德州红脖没文化，公司没几个phd,只能从书上抄了。哈哈 | m*********n
发帖数: 1819 | 4 a) asks for Pr(n+1=head | n=head)=0.5*Pr(fair coin|n=head)+1*Pr(unfair coin|
n=head)
Baysian rule: Pr(fair coin|n=head)=Pr(fair coin & n=head)/Pr(n=head)
=0.5/(1+0.5)=1/3
so Pr(unfair coin|n=head)=2/3
so 0.5*1/3+1*2/3=5/6 | J****g
发帖数: 103 | 5 I got 3/4.
Transition Matrix = [3/4, 1/4; 1/2, 1/2]. Yes, Markov.
coin|
【在 m*********n 的大作中提到】
: a) asks for Pr(n+1=head | n=head)=0.5*Pr(fair coin|n=head)+1*Pr(unfair coin|
: n=head)
: Baysian rule: Pr(fair coin|n=head)=Pr(fair coin & n=head)/Pr(n=head)
: =0.5/(1+0.5)=1/3
: so Pr(unfair coin|n=head)=2/3
: so 0.5*1/3+1*2/3=5/6
| n****e
发帖数: 629 | 6 Markov? hmm....
【在 J****g 的大作中提到】
: I got 3/4.
: Transition Matrix = [3/4, 1/4; 1/2, 1/2]. Yes, Markov.
:
: coin|
| J****g
发帖数: 103 | 7 啊， 错啦？我再去看看。
【在 n****e 的大作中提到】
: Markov? hmm....
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