Problem "I [8 points]. A box contains on blue and m red balls. You draw 11 balls with replacement. Using central limit theorem, estimate the minimum value of n in order to be at least 95% sure that the proportion of drawn blue balls is at least {145 but not more than 0.55. Problem 8 [8 points]. Given that X1, X2, X3, ..., Xn is a random sample from X ~ Poisson(1), derive the maximum likelihood estimator for 1.Problem 9 [8 points]. Let X1, X2, X 3, be a sequence of continuous random variable such that: mm = 212-11'1' Show that X\" converges in probability to 0