If x is a binomial random variable, compute P(x) for each of the following cases:   (a) P(x\leq 6) , n = 8 , p = 0.6   (b) P(x> 2) , n = 3 , p = 0.7 (c) P(x< 3) , n = 7 , p = 0.7

For independent random variables X and Y, we have var(X -Y) = var(X)-var(Y ). * true False

If P(B) = ² and P(A'^B) = 12, for two events A and B, find P(A/B).

Let E and F be two events of an experiment with sample space S. Suppose P(E) = 0.46, P(F^) = 0.65, and P(E U F) =0.7. Calculate the probabilities below. (a) P(E) = (b) P(F) (c) P(E n F) =

In the first hour of customers using the app they served 180 customers. STACO decided to treat this hour as 60 non-overlapping intervals of one minute each. They then assumed they could model the number of customers served each minute by independent and identically distributed Poisson Random Variables. They called the number of customers served in the ith minute X₁, so X₁ + X₂ + ... + X60 180, X₁~ Poisson(X), and X; and X, are independent if i j. - STACO used this to compute an estimated 95% confidence interval and then told Coffee Kart that they could claim to serve an average of three customers per minute. = i Recall that the maximum likelihood estimator of A is A X. Using the same assumptions as STACO and assuming that n is large enough to apply the Central Limit Theorem, calculate an estimated 95% confidence interval for X. ii Do you agree with the assumptions made by STACO. Justify your answer.