1. a) A company which sells corn flakes is conducting a contest. In each box of cornflakes, the company has put a random card. There are 50 distinct cards which must be collected in exchange for a prize. What is the probability distribution of the random variable t_i which is the time taken to collect the i^th card after (i 1 )^th cards have been collected and what is its expected value? (Hint: The order of collecting the cards is not important.)

select one:

a) Poisson, mean = (1/n-i )

b) geometric , mean = (1/n)

c) geometric, mean = { n/ ( n-i+1) }

d) Poisson, mean = { (n-i+1)/n}

1. b) 20% of tables reserved by customers remain vacant because the customers don't show up. To make up for the loss the restaurant takes more reservations than the number of tables they have. If the restaurant has 50 tables and has taken 52 reservations, what is the probability that it can accommodate everyone (to five decimal places)?
2. 2n light bulbs are lit at the same time. Let the lifetime of each light bulb be an exponential distribution with parameter 4k . Let X be the minimum of the lifetime of all of the 2n light bulbs. The PDF of X is .