# STA013 12 PROBABILITY MASS FUNCTION

STA013 12 PROBABILITY MASS FUNCTION
A home security system is designed to have a 99% reliability rate. Suppose that nine home equipped with this system experience an attempted burglary. Find the probability that at least one of the alarms are triggered.
1- (.999 ) – 9* (.998 )* (.01)
1- (.999 )
1- (.019 )
1- (.019 ) – 9* (.018 )* (.99)
Flag question: Question 8
Question 8
1 pts
A home security system is designed to have a 99% reliability rate. Suppose that nine home equipped with this system experience an attempted burglary. Determine the average number of alarms that are triggered and the variance of the number of alarms that are triggered.
mean = .99, variance = .01
mean = 0.0891, variance = .09
mean = .09, variance = 0.0891
mean = 8.91, variance = 0.0891
Flag question: Question 9
Question 9
1 pts
A box contains 5 white balls and 6 black balls. Three balls are selected at random one by one with replacement. Let X be the number of black balls selected. Find E[X].
Hint: Notice that we have a Binomial experiment.
1
12/11
18/11
15/11
2
Flag question: Question 10
Question 10
1 pts
Let X be a discrete random variable given by the following PMF. Calculate E[X2 ].
X = k
P(X=k)
k=-8
0.8
k=8
0.2
64
-5.2
.8
0
Flag question: Question 11
Question 11
1 pts
According to a study, the percentage of households with vehicles in Boston, Massachusetts, is 65%; in Cambridge, Massachusetts, 70%; and in Worceter, Massachusetts, 80%. Suppose owning a vehicle in these three cities are independent of each other. If a household from each city is randomly selected, What is the probability that none of the three households has a vehicle.
0.240
.150
0.021
0.364
Flag question: Question 12
Question 12
1 pts
A box contains two red, two blue, and four green marbles. Three marbles are selected at random with replacement from the box. Let
A={all selected balls are blue}
Find P(A).
1/4
1/8
1/2
1/64

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