3. If X and Y are independent uniform (0, 1) random variables, show that2(a + 1)(a + 2)E[|X - Yº] =for a>0

X and Y are independent U(0,1) random variables:Objective: Show that:

Answered: 3. If X and Y are independent uniform…

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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2. Suppose one has n non-degenerate random variables X1, X2,, X, so that X1+ X2 + · · · + Xn = L for some constant L. (Recall that a random variable is non-degenerate if it is not a constant in disguise.) Show that there must be at least one pair of indices i j so that p(X;, X;) < 0.
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1. (Independence). (i) Recall that given events A, B,C, we have that P(AUBUC) = P(A)+ P(B)+ P(C) – P(An B) – P(AnC)– P(BnC) + P(AN BnC). (4.1) Prove that whenever events A, B,C are mutually independent, we have that P(AUBUC) = 1– P(A^)P(B^)P(C*) = 1– (1– P(A)) · (1 – P(B)) · (1 – P(C)) (and the probability in question can be calculated considerably faster than with the use of the formula (4.1)). (ii) The probability that A hits a target is 2/5, the probability that B hits it is 5/9, and the probability that C hits the target is 3/7. Use (i) to find the probability that the target will be hit if A, B, and C each shoot at the target. (iii) Suppose that the probability that a soldier firing his personal weapon hits an enemy warplane is p > 0. Show then, arguing as in (i), that the probability that the warplane is hit at least once when n > 2 soldiers shoot at it is 1- (1 — р)". (4.2) Evaluate the probability in (4.2) in the case when p = 0.0006 and n = 750, and then round your result to a…
7. Suppose that the joint p.d.f. of two random variables X and Y is as follows: (4 – 2x – y) for x > 0, y > 0, f(x, y) = and 2x + y 2|X = 0.5).
What is the definition of independence for two discrete random variables X and Y? X and Y are independent if and only if P(X= x) = P(Y= y) for all x and y. OX and Y are independent if and only if P(X = x Y = y) = P(X = x)*P(Y= y) for all x and y. X and Y are independent if and only if P(X= x | Y = y) = P(X = x) for all x and y. Previous

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3. If X and Y are independent uniform (0, 1) random variables, show that 2 for a > 0 (a + 1)(a + 2) E[|X – Y|ª] -