The number of pumps in use at both a six-pump station and a four-pump station wi
ID: 1720410 • Letter: T
Question
The number of pumps in use at both a six-pump station and a four-pump station will be determined. Give the possible values for each of the following random variables. T = the total number of pumps in use X the difference between the numbers in use at stations I and 2 U the maximum number of pumps in use at either station Z = the number of stations having exactly two pumps in use A mail-order computer business has five telephone lines. Let -V denote the number of lines in use at a specified time Suppose the pntfof X is as given in the accompanying table. Calculate the probability of each of the following events. at most 3 lines are in use fewer than 3 lines are in use J !at least 3 lines are in use) between 2 and 5 lines, inclusive, are in use) {between 2 and 4 lines, inclusive, are not in use} {at least 4 lines are not in use} Suppose that in one area in California. 40% of all homeowners are insured against earthquake damage. Four homeowners are to be selected at random; let A'denote the number among the four who have earthquake insurance Find the probability distribution of and associated What is the most likely value for A? What is the probability that at least two of the four selected have earthquake insurance? An insurance company offers its policyholders a number of different payment options. For a randomly selected policyholder, let .V - the number of months between successive payments. The cdf of X is as follows: What is the pmf of X? Using just the cdf. compute P(3 6).Explanation / Answer
(1)
(a)
T is the total number of pumps in both stations
six in first station and four in second station
so, total pumps = 6+4=10
and we can get
T={0,1,2,3,4,5,6,7,8,9,10}
(b)
X is the difference between them
difference =6-2=4
or
difference =2-6=-4
so, we would get
X={-4,-3,-2,-1,0,1,2,3,4}
(c)
U is the maximum number of pumps in use at either station
we know that maximum number of pumps is at station-1
and number of pumps =6
U={0,1,2,3,4,5,6}
(d)
Z is the number of stations with two pumps in operation
Z={0,1,2}