Consider a renewal process with the lifetimes X1, X2, ... having the probability density function f(x) = 0.125. (4 — x)for 0 < x < 4.Determine the asymptotic expression for the probability distribution of excess life Yt:lim P(2.75) =t→∞Determine the limiting mean excess life:lim E[Y] =t→∞=

To solve the given problem, there are a series of steps that must be followed. The problem deals…

Answered: Consider a renewal process with the…

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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Let X denote 0.025 × the ambient air temperature (˚C) and let Y denote the time (min) that it takes for a diesel engine to warm up. Assume that (X, Y) has joint probability density function f(x,y) = cx (1 − x)(6 + 5x − 4y), for 0 < x < 1, 0 < y < 0.5. Find the conditional pdf of Y, given X = x. Compare this to the marginal pdf of Y. Are air temperature and engine warm-up time independent?
Let X denote 0.025 × the ambient air temperature (˚C) and let Y denote the time (min) that it takes for a diesel engine to warm up. Assume that (X, Y) has joint probability density function f(x,y) = 1.6x (1 − x)(6 + 5x − 4y), for 0 < x < 1, 0 < y < 0.5. Find the conditional pdf of Y, given X = x. Compare this to the marginal pdf of Y. Are air temperature and engine warm-up time independent?
Suppose that X, Y are jointly continuous with joint probability density function f( x, y){ xe^-x(1+y), ifx >0 and y >00, otherwise. (a) Find the marginal density functions of X and Y. (b) Calculate the expectation E[XY]. (c) Calculate the expectation EIX/(1+ Y )1. (e) Determine if the random variables X and Y in this exercise are independent.
A rectangular plate with insulated surface is 10 cm. wide and so long compared to its width that it may be considered infinite length. If the temperature along short edge y = 0 is given u(x,0) = 8 sin(px/ 10) when 0 <x <10, while the two long edges x = 0 and x = 10 as well as the other short edge are kept at 0o C, find the steady state temperature distribution u(x,y).
If X is exponentially distributed with parameter λ and Y is uniformly distributed on the interval [a, b], what is the moment generating function of X + 2Y ?
Step 3: Expression for density function of T, in the convolution, isn't (t-s1) term extra?
Suppose you choose a real number X from the interval [2, 10] with a density function f(x) = 1/48x. Find P(X > 5)
If X is uniformly distributed over (0,1), find the density function of Y = eX
X follows a gamma distribution with PDF f(x) = 4xe-2x , where X > 0(a) Derive E(Xn ).
Suppose that X and Y have a joint probability density function f(x,y)= 1, if0<y<1,y<x<2y; 0, otherwise. (a) Compute P(X + Y less than or equal 1). (b) Find the marginal probability density functions for X and Y , respectively. (c) Are X and Y independent?
For the probability density function f(x) = 3x^2 on [0,1], find: V(X)
Suppose X and Y have a joint density function of f(x,y)=6x2y, 0<x<1, 0<y<1. Find P(X+2Y<1).

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