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.

Question

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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The Answer of 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.

Let Y Be a Bernoulli Random Variable with Success Probability