Introduction to Econometrics 3rd Edition by James Stock, Mark Watson

تمرين 35

Y i ,i = 1,..., n , are i.i.d. Bernoulli random variables with p = 0.4. Let
denote the sample mean.
a. Use the central limit to compute approximations for
i. Pr(
0.43) when n = 100.
ii. Pr(
0.37) when n = 400.
b. How large would n need to be to ensure that Pr(0.39
0.41) 0.95 (Use the central limit theorem to compute an approximate answer.)