For Company A there is a 60% chance that no claim is made during the coming year. If one or more claims are made, the total claim amount is normally distributed with mean $10,000 and standard deviation $2,000. For Company B there is a 70% chance that no claim is made during the coming year. If one or more claims are made, the total claim amount is normally distributed with mean $9,000 and standard deviation $2,000. Assume that the total claim amounts of the two companies are independent. What is the probability that in the coming vear Company R's total claim amount will
For Company A there is a 60% chance that no claim is made during the coming year. If one or more claims are made, the total claim amount is normally distributed with mean $10,000 and standard deviation $2,000. For Company B there is a 70% chance that no claim is made during the coming year. If one or more claims are made, the total claim amount is normally distributed with mean $9,000 and standard deviation $2,000. Assume that the total claim amounts of the two companies are independent. What is the probability that in the coming vear Company R's total claim amount will
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:For Company A there is a 60% chance that no claim is made during the coming year.
If one or more claims are made, the total claim amount is normally distributed with
mean $10,000 and standard deviation $2,000. For Company B there is a 70% chance
that no claim is made during the coming year. If one or more claims are made, the
total claim amount is normally distributed with mean $9,000 and standard deviation
$2,000. Assume that the total claim amounts of the two companies are independent.
What is the probability that, in the coming year, Company B's total claim amount will
exceed Company A's total claim amount?
Let X be a continuous random variable with density function
(2x, x22
Ax) =;
0,
otherwise
1
for 0<y<1.
X-1
Determine the probability density function of Y =:
Claim amounts at an insurance company are independent of one another. In year one,
claim amounts are modeled by a normal random variable X with mean 100 and
standard deviation 25. In year two, claim amounts are modeled by the random
variable Y = 1.04X + 5. Calculate the probability that a random sample of 25 claim
amounts in year two has an average between 100 and 110.
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