2. We have n = 100 many random variables X;'s, where the Xi's are independent and identically distributed Bernoulli random variables with Р = 0.5 (E(X₂)=p and var(X;)=p(1-p)). n a. What distribution does X; follow exactly (sum of independent Bernoulli random variables)? State the type of distribution and what the parameter is. i=1 n b. Using the central limit theorem, what approximate distribution does X = X, follow? State the type and the mean and variance. n i=1 c. What is the approximate probability that X = [X; is greater than 0.5? Write down the integral using proper notation and use empirical rule or pnorm function in R to obtain numeric i=1 answer.

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