A long-distance cyclist's back tire sometimes pops during long rides. because the cyclist knows that her tire has a tendency to pop, she carries a repair kit with her. Let X be the number of times that the cyclist's tire pops during a 70 mile ride. X is either 0,1,2 or 3. The probability mass function of X is given in the table below:
where a is unknown positive value, assume p(x) = 0 if x ?/ 0, 1, 2, 3
(a) What is the probability that the tire pops twice during a 70 mile ride?
|
x
|
0
|
1
|
2
|
3
|
|
P(x)
|
.4
|
a
|
3a
|
.16
|
(b) What is the expected value of the number of times that the cyclist's tire pops during a 70 mile ride?
(c) Each time her tire pops, the cyclist spends 10 minutes repairing her tire. What is the expected value of time that she spends fixing her tire on a single ride?