A longdistance cyclists baric tire sometimes pope during lon

A long-distance cyclist\'s baric tire sometimes pope 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 a. The probability mass function o: X is given in the table below where it is unknown positive value, assume p(z) = 0 if x 0.1.2.3 What is the probability that the tire pops twice during a 70 mile ride? What is the expected value of the number of times that the cyclist\'s tire pops during a 70 mile ride? 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?

Solution

a)

The probabilities must add up to 1. Thus,

0.4 + a + 3a + 0.16 = 1

4a = 0.44

a = 0.11

Thusm

P(2) = 3a = 0.33 [answer]

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b)

Consider the table:      
      
x   P(x)   x P(x)
0   0.4   0
1   0.11   0.11
2   0.33   0.66
3   0.16   0.48
      
Totals       1.25
       =E(x)
      
Thus,      
      
E(x) =    1.25   [ANSWER]

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c)

Thus,

E(10x) = 10E(x) = 10*1.25 = 12.5 minutes [ANSWER]