Let X and Y be continuous randomvariables with joint density functionf(x,y) = 2(x+y)/3.53 on the interval 0 <y

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Answered: Let X and Y be continuous random…

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 and Y be two random variables with joint density function f(x,y) = (3 − x + 2y) / 60, for 1 < x < 3, 0 < y < 5. Find the marginal density functions. (Check that they are nonnegative and integrate to 1 before continuing further) Are X and Y independent? Explain.
The number of minutes that train is early or late can be modeled by a random variable whose density is given by: g(t) = {(1/972)(81 − t^2), −9 ≤ t ≤ 9, 0 elsewhere, where negative values indicate the train arriving early and positive values indicate the train arriving late. a. Find the probability that one of the train trips will arrive more than 5 minutes early. b. Find the probability that one of the train trips will arrive between 1 and 8 minutes late. c. Without integration, give the expected number of minutes early/late. Examination of the graph and recollection of properties of integrals will allow this.
Let X be a continuous random variable with probability density function given by f(x)=x/2 ; Osxs2 and f(x)=0 otherwise. Then the second moment about the zero is 8 4 0.75 2/9 2.
The probability density function of a distribution is given by x f(x) = exp(-7). Use differentiation to show that the probability density function has a maximum at x = 0. The moment generating function of a distribution is M(t) = (q + pet)", where p € [0, 1], q = 1 - p and n is a positive integer. Use the moment generating function to find the mean and variance of the distribution in terms of p, q and n.
The diameter of a particle of contamination (in micrometers) is modeled with the probability density function 2 f(x)= = x3 for x > 1 . What is the probability that the diameter of the particle of contamination is below 2 micrometers?
The lifetime, in years, of some electronic component is a continuous random variable with the density f(x) X ≥ 1 0, x < 1 Find the cdf F(x), and compute the probability for the lifetime to exceed 5 years.

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Let X and Y be continuous random variables with joint density function f(x,y) = 2(x+y)/3.53 on the interval 0 < y < x < 3.5. Calculate the probability that X < 2. i.e. find P(X <2). Enter your answer to three decimal places.