For each n 1, let X_n be an exponential random variable with parameter n, and Yn be a normal random variable with mean zero,

For each ~ > I , let In be an exponential random variable with parameter ~ , and In be a normal random variable with mean zero , and variance_ ( a ) Show that In converges to zero in probability as ~ goes to infinity . ( b ) Show that ~ In converges in distribution to a standard normal random variable as n goes to infinity