Suppose we have a biased coin that comes up heads 55% of the time. We perform...

Suppose we have a biased coin that comes up heads 55% of the time. We perform an experiment where we toss the coin until the first tails appears. Let T be the number of tosses until the first tails. What is the expected value and standard deviation for T? What is the probability that it takes 5 or more tosses before the first tails appears?

Expert Solution

suppose we have series of independent trials or repetetion and in each trial the probability of succes p=0.45 (=1-q=1-55%=0.45)i.e probability of obtaining tails. then the probability that there are t failures (obtaining heads is taken as failure with probability q=55%=0.55) preceeding first success is given by (q^t)p

this is nothing but the geometric distribution so, we will use geometric distribution p.m.f q^t p ,q=1-p

=0.0.05033(approx.)

orchestra answered 2 years ago

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