Essay
Let Y be a Bernoulli random variable with success probability Pr(Y = 1)= p,and let Y1,... ,Yn be i.i.d.draws from this distribution.Let
be the fraction of successes (1s)in this sample.In large samples,the distribution of
will be approximately normal,i.e. ,
is approximately distributed N(p,
).Now let X be the number of successes and n the sample size.In a sample of 10 voters (n=10),if there are six who vote for candidate A,then X = 6.Relate X,the number of success,to
,the success proportion,or fraction of successes.Next,using your knowledge of linear transformations,derive the distribution of X.
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X = n ×
.Hence if
is distrib...View Answer
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