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Let X be a random variable with the following function f(x) = A: if x = 1,2,3, . then otherwise the mode of the pdf f(x) is a- 2 b- 3 e-1

Let X be a random variable with the following function f(x) = A: if x = 1,2,3, . then otherwise the mode of the pdf f(x) is a- 2 b- 3 e-1

A First Course in Probability (10th Edition)
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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5) Let X be a random variable with the following function f(x) = : if x = 1,2,3, . then otherwise the mode of the pdf f(x) is e- 1 : 0<x<3 and 0<y<1¸ then fr0) = a- 2 b- 3 6) Define a joint pdf by fx.r(x,y) = otherwise a- y? b- 3y2 7) Let X a random variable with pmf P(X = xN) =. x = 1,2, . N, and let Y = 3X +7, where a, be then EY = %3D N+1 a- 3 +7 b- 3 N+1 8) Let X be a random variable, and let g,(x) and g2(x) any two functions whose expectations exist, whereg, (x) = x2, x = 1,2,3,4, undg,(x) = x, x = 1,2,3,4, then: a- Eg, (x) = Eg,(x) b- Eg,(x) > Eg,(x) e- Eg,(x) < Eg,(x) 9) Let the continuous random variables X and Y have joint pdf f(x, y) = e-y ,0 <x< co, 0 < y < o, then f(x/y) = b-e a- ey 10) Var(2) = a- 0 b-1 e-4
Transcribed Image Text:5) Let X be a random variable with the following function f(x) = : if x = 1,2,3, . then otherwise the mode of the pdf f(x) is e- 1 : 0<x<3 and 0<y<1¸ then fr0) = a- 2 b- 3 6) Define a joint pdf by fx.r(x,y) = otherwise a- y? b- 3y2 7) Let X a random variable with pmf P(X = xN) =. x = 1,2, . N, and let Y = 3X +7, where a, be then EY = %3D N+1 a- 3 +7 b- 3 N+1 8) Let X be a random variable, and let g,(x) and g2(x) any two functions whose expectations exist, whereg, (x) = x2, x = 1,2,3,4, undg,(x) = x, x = 1,2,3,4, then: a- Eg, (x) = Eg,(x) b- Eg,(x) > Eg,(x) e- Eg,(x) < Eg,(x) 9) Let the continuous random variables X and Y have joint pdf f(x, y) = e-y ,0 <x< co, 0 < y < o, then f(x/y) = b-e a- ey 10) Var(2) = a- 0 b-1 e-4
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