1. (3 POINTS) An insurance policy pays a individual $500 per day for up to 3 days of hospitalization and $100 per day for each day of hospitalization thereafter. The number of days of hospitalization is a random variable X with
P(X=x) = (6-x)/15, if x = 1,2,3,4,5.
Calculate the expected payment for hospitalization under this policy.
2. (4 POINTS) An insurance policy reimburses a loss up to a benefit limit 0f $10. There is no deductible. The policyholder’s loss X (in $) has probability density function
f(x) = 2/ x^3, if x > 1; and f(x) = 0, otherwise.
What is the expected value of the benefit paid under the insurance policy?
Hint: Find E(Y) where Y = min (X,10).
3. (4 POINTS) The probability distribution of claim sizes for an auto insurance policy is as follows:
Claim Amount (in $): 200 300 400 500 600 700 800
Probability: 0.15 0.10 0.05 0.20 0.10 0.10 0.30
What percentage of the claims is within one standard deviation of the expected claim size?
4. (4 POINTS) Compute the expected value and the standard deviation of the number of spades in a poker hand.
(1). Let X denote the numbe of days in the hospital and Y the total payment, the given information can be summarized in the following table:
Hence, the expected payment is
(2). The amount paid under this policy is
The expected amount paid is
(3).
The mean claim size is
The second moment of the claim size is
Therefore, the variance of the claim size is
The standard deviation is
The claim sizes within one standard deviation of the mean claim size of 550 are those claim sizes between
550 - 217.9 = 332.1 and 550 + 217.9 = 767.9
Those claim sizes are 400, 500, 600 and 700. The total probability of those claim sizes is
0.5 + 0.20 + 0.1 + 0.1 = 0.45
Thus the answer is 0.45 or 45 %
(4). Define a random variable X as the number of spades in a poker hand. We know that
1. (3 POINTS) An insurance policy pays a individual $500 per day for up to 3...
An insurance policy pays for a random loss X subject to a deductible of 550. The loss amount is modeled as a continuous random variable with density function 4500 for x > 500 f(x) = { otherwise Determine the expected payment made under this insurance policy.
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1. An individual who has car insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The probability distribution of Y is given in the table below: Ply) 0. 600 .25 0.10 0.05 a. Determine the expected value of Y, that is E(Y). [4 points) E(Y)=0(0.6) + 110.25) +2(0.10) +3(0.05) E(Y)=0.6 b. Suppose an individual with Y violations incurs a surcharge of $100XY?....