6.82 If Y is a continuous random variable and m is the median of the distribution, then m is suchthat P(Y ≤m) = P(Y ≥ m) = 1/2. If Y₁, Y₂, ..., Y, are independent, exponentially dis-tributed random variables with mean ß and median m, Example 6.17 implies that Y(n) =max (Y₁, Y₂, ..., Yn) does not have an exponential distribution. Use the general form of Fy) (y)to show that P(Y(n) > m) = 1- (.5)".

Answered: .82 If Y is a continuous random…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Problem 1P

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.11 Suppose X is a continuous-type random variable with CDF Fx. Let Y be the result of applying Fx to X. that is, Y = Fx(X). Find the distribution of Y.
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Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
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25. Suppose X is a random variable distributed with mean u and standard deviation a > 0. If the random variable Y is defined as Y = u(X - uX)/a, then E(Y) is: a. 0 b. 1 d. E(X)
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34. Suppose that X is a random variable with MGF M(t) = (1/8)e + (1/4)e + (5/8)e. (a) What is the distribution of X? (b) What is P[X= 2]?
4.2 The probability distribution of the discrete random variable X is f(x) = 3 (*)*** Find the mean of X. 3-x (¹)ª (²³)³—ª, x = 0, 1, 2, 3.
2. Suppose that X and Y are independent random variables, both with the standard normal distribution i.e. X, Y~ N(0, 1). For pe [-1, 1], define Z:=√1-p²X + pY. Show that E[Z|Y] =pY.

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