021.pdr (714 KB)Z denotes the random present value for an insurance contract issued on the independentlives (x), r > 0 and (y), y > 0, wherevT(), if T(y) > T(x)Z =0,{otherwise.Given that• (r) is subject to a constant force of mortality of 0.07;• (y) is subject to a constant force of mortality of 0.09;• The force of interest is a constant d 0.06.Compute the variance Var(Z).

Given Z¯=vTy, if Ty>Tx 0 , otherwise (x) is subject to a constant force of mortality…

Answered: Z denotes the random present value for…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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2. Y1, Y2, ..., Yn are i.i.d. exponential random variables with E{Yi} = 1/θ. Find thedistribution of Y =1 nPiYi.
A certain brand of upright freezer is available in three different rated capacities: 16ft3, 18 ft3, and 20 ft3. Let X = the rated capacity of a freezer of this brand sold at acertain store. Suppose that X has pmfx 16 18 20p(x) .2 .5 3a. Compute E(X), E(X2), and V(X).b. If the price of a freezer having capacity X is 70X – 650, what is the expectedprice paid by the next customer to buy a freezer?c. What is the variance of the price paid by the next customer?d. Suppose that although the rated capacity of a freezer is X, the actual capacityis h(X) = X - .008X2. What is the expected actual capacity of the freezer purchasedby the next custom
3.) Suppose X has probability generating function GX(t) = 0.2 + 0.3t + 0.1t2 + 0.4t3. What is P(X = 2)? What is P(X = 0)?
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For a hypothesis test of H0:μ=μ0H0:μ=μ0 against the alternative Ha:μ<μ0Ha:μ<μ0, the z-test statistics is found to be 2.00. This finding is a.significant at neither the 0.01 nor the 0.05 levels. b.significant at the 0.01 level but not at the 0.05 level. c.significant at both the 0.01 and the 0.05 levels. d.not large enough to be considered significant. e.significant at the 0.05 level but not at the 0.01 level.
The moment generating function of the random variable X is given by mX(s) = e2e^(t)−2 and the moment generating function of the random variable Y is mY (s) =(3/4et +1/4)10. If it is assumed that the random variables X and Y are independent, findthe following:(a) E(XY)(b) E[(X − Y )2](c) Var(2X − 3Y)
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Q1- What is the probability that the number of heads and are equal it a lait coin is tossed, a)15 times b)20 times Q2- Suppose the joint pdf of X and Y is given by: F xy (x y)={ ex +3y, if 0<x< 1 and 0<y<1 0 otherwise find E(x) . Q2- Suppose X is a random variable with E(X) = 5 and Var(X) = 2. What is E(X)?
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X1 and X2 are independent random variables such that Xi has PDF fXi(x)={λiexp(−λix) when x≥0, 0 otherwise}. What is P[X2<X1]?
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