Mathematics, 28.05.2020 04:00, gabw2758

We have n = 100 many random variables Xi ’s, where the Xi ’s are independent and identically distributed Bernoulli random variables with p = 0.5 (E(Xi)=p and var(Xi)=p(1-p)). a. What distribution does Pn i=1 Xi follow exactly (sum of independent Bernoulli random variables)? State the type of distribution and what the parameter is. b. Using the central limit theorem, what approximate distribution does X¯ = 1 n Pn i=1 Xi follow? State i the type and the mean and variance. c. What is the approximate probability that X¯ = 1 n Pn i=1 Xi is greater than 0.5? Write down the integral using proper notation and use empirical rule or pnorm function in R to obtain numeric answer.

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We have n = 100 many random variables Xi ’s, where the Xi ’s are independent and identically distrib...