Question
In: Math
Car battery The mileage of a car battery is exponentially distributed with a mean value of...
Car battery
The mileage of a car battery is exponentially distributed with a mean value of 10000 km.
(a) What is the probability of a 5000 km trip without replacement of the battery?
(b) What is the maximum length of travel that can be terminated with 90% probability without replacing the battery?
(c) Determine the median, the mean and the variance of the mileage of the battery
Solutions
Expert Solution
(a)
Probability Density of X is given by:
,
forx > 0
between limits 5000 to 
Applying limits, we get:
So,
Answer is:
0.6065
(b)
between the limits x to
Applying limits, we get:
Taking logarithm on both sides, we get:
So,
x = 1054
So,
Answer is:
1054
(c)
(i) Mean is given by:
between limits 0 to
Applying limts, we get:
Mean = 10000
(ii) Median is given by:
between limits 0 to x.
Applying limits,we get:
i.e.
Taking logarithm on both sides, we get:
So,
x = 6931
So,
Answer is:
6931
(iii)
between limits 0 to
Applyinglimits, we get:
E(x2)=200000000
So,
Variance = E(x2)- (E(x))2
= 200000000 - 100002
= 100,000,000
So,
Answer is:
100,000,000
milcah answered 7 months agoRelated Solutions
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