Reference no: EM132855880

Instructions: Answer the following in a mathematically sound argument (proof) using combinations of English / symbols as needed.

T1. Suppose two cookie jars each have 25 cookies and whenever Cookie Monster gets hungry, he selects a cookie uniformly at random from either one. We are interested in computing the chance of one jar being close to empty when the other is eaten entirely. Let C denote the number of cookies left in a jar when the other jar becomes empty. Find the probability that there are k cookies left, that is what is P(C=k)?

T2. Two restaurants compete against one another for a pool of 10,000 local potential patrons. Assuming people tend to choose between the two restaurants at random and independently, use a binomial model to find how many seats S our restaurant should have such that the probability of turning a customer away due to being at capacity is less than 1%.

T3. Given that X1Poisson(1) and X2Poisson(2) prove that X1+X2Poisson(12), that is prove that the sum of Poisson distributions is itself also Poisson. This property also holds for normal distributions also.