Consider three types of claims: A, B and C. Let XẠ denote the randomvariable for the size of a randomly chosen claim of type A, and let XBand Xc denote the corresponding random variables for claims of typesB and C, respectively.Assume that XA, XB and Xc are exponentially distributed with parame-ters XA = 0.002, AB = 0.001 and Xc = 0.005, respectively.An insurance company has a portfolio of policies with 10% of claims oftype A, 20% of type B, and the remaining claims of type C.Let X denote the random variable for the size of a claim chosen at ran-dom from all those on policies in the portfolio.100) the probahility thata lanaomiy thoeerolaim(a)Caloulat AiS greater than 100(b) Calculate E[X|Type] for types A, B and C.

Exponential distribution is a continuous distribution that observes and waits for an event to occur.…

Answered: Consider three types of claims: A, B…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Calculate the mean value (expected value) of the following discrete variable x: x-0, 1, 2, 3, 4, 5, 6 %3D p(x) 3D 0.2, 0.2, , 0.05 0.15,0.15, 0.15, 0.1
1. The random variables X and Y describe the outcome of two independent tosses with a dice. Let Z = X+Y be the sum of the results. Determine (a) The probability distributions for X, Y and Z. (b) H(X), H(Y) and H(Z). (c) H(YX), H(Z|X) and H(X|Z). (d) I(X;Y) and I(X; Z).
Given n independent policyholders with individual loss random variables X1, X2, ., Xn, such that the expected value of any policyholder's loss is pph and the variance is o. If the insurer is providing these n policyholders with insurance, find the following (the detailed steps are required): 1. The expected value of the insurer's average loss per policy; 2. The variance of the average loss per policy.
What does the memoryless property refer to? An event cannot occur if it has already occured within a recent specified time period. The distribution of the time until an event does not depend on how much time has already passed. The occurrence of an event is independent of the number of times that event has already occurred. None of the above.
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1. A random variable x has the following probability function : -2 -1 1 3 P(x) 0.1 K 0.2 2k 0.3 3k Find the value of k, calculate mean and variance.
Why is the probability that a continuous random variable equals a specific number zero? That is, why is P(X=b)=0 for any number b?
(a). Derive the theorem of total chance of occurrence of engineering events. (b). If Faculty of Engineering and Technology is located south of the land of Malete and experiences Wet and Dry seasons yearly. Assume the Wet season in the vicinity of the building lasts for 1/3 of the year, and the Dry season for 2/3 of the year. The chances of rain falling during the wet and dry seasons are 3/4 and 1/6, respectively. i. If you visit the engineering building on a random day of the year, what is the chance that it will rain on arrival? If you visit the engineering building on a random day, and it rains on arrival. What is the chance that your visit is during the wet season? ii.

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