Question

Problem 38)

llung the ot number typists A, B, and C. If it is of errors made is a Poisson random variable with ped by B, then the number of errors is a Poisson random variable it typed by C, then it is a Poisson random variable with mean 2o: it t mean with Let X denote the number of errors in the typed manuscript. Assume that each npist is equally likely to do the work opist is equa a) Find &x) )Find Var) seY is uniformly distributed on (0. 1), and that the conditional distribution of X given that yy is uniform on (O. y). Find ELX] and Varx). 3 A deck of n cards, numbered 1 through n. is randomly shuffled so that alln pussible permutations are equally likely. The cards are then turned over one at a ime until card number 1 appears. These upturned cards constitute the first cycle. We now determine (by looking at the upturned cards) the lowest numbered card that has not yet appeared, and we continue to turn the cards face up until that card appears. This new set of cards represents the second cycle. We again determine

Answer 1

Answer:

38.

Since Y lies between O and 1, the expectation is obtained as: E(x)-Js(x)dr -ln(x) and V-X. The value is obtained as: Solve the integration of the above term by taking u 4 4 4 The expectation of the random varlable, X, Is 4

Variance is obtained by the formula: 4 After putting the limits, the variance can be obtained as: 9 16 9 16 144 The variance of the random variable, X, Is 144