please send handwritten solution for Q 4

When doing polling, for instance to gure out how popular a given candidate is, a common trick is to just ask N many people whether they support that candidate, and take the support to be the [action of people who say yes: if 70 people support the candidate out of 100 asked, we estimate the support at 70% or 0.7. Suppose that the probability a person supports a candidate is p, which you do not know. Let :3\" be the fraction of N people polled who support the candidate: total supporters divided by N people polled. 1) 'What is the distribution of N a fin? 2) Show hat the expected value of 15\" is p. i.e., 15" is a valid estimator for 13. If you want your estimated value of p to be accurate, you want your 'error' on fix to be small. 3) How many people N should you poll to guarantee the expected squared error on u is less than c? 4) How many people N should you poll to guarantee the expected squared error on fur is less than a, even if you don't know p? In the previous to problems. we considered the average or expected squared error. But just because the expected error is small doesn't mean the actual error is small. 5) How many people N should you poll to guarantee the actual error on gig is less than c with 95% condence. even if you don't know p