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Fred needs to choose a password for a certain website. Assume that he will choose an 8-character password, and that the legal characters are the lowercase letters a, b, c, ..., z, the uppercase letters A, B, C, ..., Z, and the numbers 0, 1, . . ., 9. (a) How many possibilities are there if he is required to have at least one lowercase letter in his password? (b) How many possibilities are there if he is required to have at least one lowercase letter and at least one uppercase letter in his password? (c) How many possibilities are there if he is required to have at least one lowercase letter, at least one uppercase letter, and at least one number in his password?

a =1500, b=1700 what is percentage of a is b

A 12-inch bar that is clamped at both ends is to be subjected to an increasing amount of stress until it snaps. Let Y = the distance from the left end at which the break occurs. Suppose Y has the following pdf. f(y) = { (a) Compute the cdf of Y. F(y) = 0 0 y -옴) 0 ≤ y ≤ 12 1- 12 y 12 Graph the cdf of Y. F(y) 1.0 0.8 0.6 0.4 0.2 y 2 6 8 10 12 F(y) F(y) F(y) 1.01 1.0ㅏ 1.0 0.8 0.6 0.4 0.2 0.8 0.8 0.6 0.4 ཨཱུ སྦེ 0.6 0.4 0.2 2 4 6 8 10 12 (b) Compute P(Y ≤ 5), P(Y > 6), and P(5 ≤ y ≤ 6). (Round your answers to three decimal places.) P(Y ≤ 5) = P(Y > 6) = P(5 ≤ y ≤ 6) = (c) Compute E(Y), E(y²), and V(Y). E(Y) = in E(Y2) v(x) = in 2 2 2 4 6 8 10 12 y 2 4 6 8 10 12

A restaurant serves three fixed-price dinners costing $12, $15, and $20. For a randomly selected couple dining at this restaurant, let X = the cost of the man's dinner and Y = the cost of the woman's dinner. The joint pmf of X and Y is given in the following table. p(x, y) 15 y 12 20 12 0.05 0.10 0.35 x 15 0.00 0.20 0.10 20 0.05 0.05 0.10 (a) Compute the marginal pmf of X. x 12 Px(x) Compute the marginal pmf of Y. y Pyly) 12 15 20 15 20 (b) What is the probability that the man's and the woman's dinner cost at most $15 each? (c) Are X and Y independent? Justify your answer. X and Y are independent because P(x, y) = Px(x) · Py(y). X and Y are not independent because P(x, y) =Px(x) · Pyly). X and Y are not independent because P(x, y) * Px(x) · Py(y). X and Y are independent because P(x, y) * Px(x) · Py(y). (d) What is the expected total cost, in dollars, of the dinner for the two people? $ (e) Suppose that when a couple opens fortune cookies at the conclusion of the meal, they find the…

Let X = the time between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution with λ = 1, (which is identical to a standard gamma distribution with α = 1), compute the following. (If necessary, round your answer to three decimal places.) (a) the expected time between two successive arrivals (b) the standard deviation of the time between successive arrivals (c) P(X ≤ 1) (d) P(2 ≤ X ≤ 4) You may need to use the appropriate table in the Appendix of Tables

In each case, determine the value of the constant c that makes the probability statement correct. (Round your answers to two decimal places.) USE SALT (a) (c) 0.9842 (b) P(0 ≤ Z ≤ c) = 0.3051 (c) P(CZ) = 0.1335 You may need to use the appropriate table in the Appendix of Tables to answer this question.