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A loss X on a car has a mixed distribution with p = 0.95
Chapter 3, Problem 13E(choose chapter or problem)
Problem 13E
A loss X on a car has a mixed distribution with p = 0.95 on zero and p = 0.05 on an exponential distribution with a mean of $5000. If the loss X on a car is greater than the deductible of $500, the difference X−500 is paid to the owner of the car. Considering zero (if X ≤ 500) as a possible payment, determine the mean and the standard deviation of the payment.
Questions & Answers
QUESTION:
Problem 13E
A loss X on a car has a mixed distribution with p = 0.95 on zero and p = 0.05 on an exponential distribution with a mean of $5000. If the loss X on a car is greater than the deductible of $500, the difference X−500 is paid to the owner of the car. Considering zero (if X ≤ 500) as a possible payment, determine the mean and the standard deviation of the payment.
ANSWER:
Solution 13E
Step1 of 3:
We have a random variable X which has mixed distribution with p = 0.95 on zero and p = 0.05
on an exponential distribution with a mean of $5000.
If the loss X on a car is greater than the deductible of $500, the difference X−500 is paid to the owner of the car.
We need to determine the mean and the standard deviation of the payment by Considering zero (if X ≤ 500) as a possible payment.
Step2 of 3:
random variable X which follows exponential distribution with parameter
The probability density function of exponential distribution is given by
Mean of the Exponential distribution is given by
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