Suppose there are 100100 cards numbered 11 through 100100. Draw a card at random. Let XX be the number of digits on the card (between 11 and 33) and let YY be the number of zeros. Find \mathrm{Cov}(X, Y)Cov(X, Y).

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?

Jonathan puts $400 in a bank account. each year the account earns 6% simple interest. how much interest will be earned in 5 years?

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