Let X and Y be the number of hardware failures in two computer labs in a given month. The joint distribution of X and Y is given in the table below. x P(x, y) 0 1 2 0 0.52 0.20 0.04 y 1 0.14 0.02 0.01 2 0.06 0.01 0 (a) Compute the probability of at least one hardware failure. (b) From the given distribution, are X and Y independent? Why or why not?

answer: you need to organize this better it does not make sense.

step-by-step explanation: ?

c

step-by-step explanation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt