Homework_Assignment_8

# Homework_Assignment_8 - variance of Y. (Ans 35 / 4, 1085 /...

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Homework Assignment 8: (1) The probability of a fire in a certain structure in a given time is 0.05. If a fire occurs, the damage to the structure is uniformly distributed between 0 and 20. The claim random variable, X, represents the fire damage to the structure within the time period. Find F X (x) and f X (x), then use f X (x) to calculate the mean and the variance of X. (Ans F X (x) = .95 + x / 400, 0 x 20; f X (x) = .95 when x = 0 and 1 / 400 when 0 < x 20; E(X) = ½; Var(X) = 77 / 12) (2) In problem (1) find the mean and the variance of X using the Double Expectation Theorems. Let I be an indicator (Bernoulli random variable) for the event that a fire occurs, and use (2.2.10) and (2.2.11) with W = X and V = I. (3) Let X be the number of heads observed in five tosses of a true coin. Then, X true dice are thrown. Let Y be the sum of the numbers showing on the dice. Use the Double Expectation Theorems [(2.2.10) and (2.2.11)] to determine the mean and
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Unformatted text preview: variance of Y. (Ans 35 / 4, 1085 / 48) A contestant on a game show selects a ball from an urn containing n balls numbered from 1 to n . The number he selects is the number of true coins he tosses to determine his prize. The variance of the number of heads he obtains is 55/16. If his prize is \$1000 times the number of heads he obtains, determine his expected prize. (Ans \$2,750) (4) A fund has been established for the purpose of insuring 11,060 lives with identical mortality profiles. For each life, you are given: (i) The probability of an accidental death is 0.01, and the probability of a non-accidental death is 0.09 (ii) If death is accidental, the claim amount is 10. For other causes of death, the claim amount is 1. Calculate the amount needed in the fund so that the probability, using the normal approximation, is 95% that the fund will be sufficient to pay the death claims. (Ans 2279)...
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## This note was uploaded on 05/11/2011 for the course STOR 472 taught by Professor Charlesdann during the Spring '11 term at University of North Carolina School of the Arts.

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