Here
(a) We are to calculate Pa=P(X=3)
(b) The mean of X is given by
By the property of binomial random variable, we know that the mean oof the distribution is the product of the parameters, if
then the mean of the distribution of Z is np.
Here the mean is then given by
(c) Though Poisson random variable cannot model the distribution but considering Y as the number of tails obtained in 5 throws of a fair coin.
Hence by the law of approximation of binomial random variable to Poisson random variable, we can say
Then Pc=P(Y=3) is given by
Now we have obtained Pa= 0.087890625 and Pc=0.09326328023
i.e Pc>Pa
3- (20 points) A random experiment consists of simultaneously and independently flipping a coin five times...
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