Question: Two ballpoint pens are selected at random from a box thatcontains 3 blue pens, 2 red pens, and(3 green pens. If X is the number ofblue pens selected and Y is the number of red pens selected, find(a) the joint probability function f(x, y),(b) P[(X, Y) EA], where A is the region {(x, y)\x+y(<1}.

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Answered: Question:Two ballpoint pens are…

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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A random variable x has a probability mass function defined by P(X=x) = r(x-1). if x= 2,3 r(8-x). if x=4,5,6 0. Otherwise Write out the probability mass function. What will be the expectation and variance of x. Find P (x greater or equal to 2 and less or equal to 5).
Recall that two events A and B are called independent if p(AB) = p(A)p(B). Similarly two random variables x and y are called independent if the joint probability function f(x, y) = g(x)h(y). Show that if x and y are independent, then the expectation or average of xy is E(xy) = E(x)E(y) = µxµy.
3) Find the mean and variance of the random variable X with probability function or density f(x). (a)f(x)={k(1-x), –15xs1 O otherwise (b) ƒ(x) = k/3× , x = 1,2,3,... Note: in this problem, you need to first find the values of k.
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Q. 4 Let X and Y be two continuous random variables with following joint probability density function SK (x² + y²); 0 Y), (c) P(X +Y > 1) (b)
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