Suppose Xi, Yi, Zi, i = 1, ..., n, are independent Bernoulli random variables, with Xi ~ Bern(0), Yi ~ Bern(n), Zi ~ Bern(7), where
Suppose Xi, Yi, Zi, i = 1, ..., n, are independent Bernoulli random variables, with Xi ~ Bern(0), Yi ~ Bern(n), Zi ~ Bern(7), where 0, n, T E (0, 1). Define S = > Xi, T = EL XiYi and U = Et-1 XiZi. (a) Find Cov( S, T) and Cov(T, U). (b) Show that 7/S converges in probability to n as n -+ 00
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