A box contains six cards, labeled 1, 2, 2, 3, 3, and 3. Two cards are chosen at random, with the first cardbeing replaced before the second card is drawn. Let X represent the number on the first card, and let Yrepresent the number on the second card.a. Find the joint probability mass function of X and Y.b. Find the marginal probability mass functions px (x) and py(y).c. Find μχ and μγ·d. Find XY.e. Find Cov(X, Y).

There are six cards in a box - 1,2,2,3,3,3 Two cards are drawn with replacement from the box. X…

Answered: A box contains six cards, labeled 1, 2,…

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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In a piston assembly, the specifications for the clearance between piston rings and the cylinder wall are very tight. In a lot of assemblies, let X be the number with too little clearance and let Y be the number with too much clearance. The joint probability mass function of X and Y is given in the table below: y x 0 1 2 3 0 0.15 0.12 0.11 0.10 1 0.09 0.07 0.05 0.04 2 0.06 0.05 0.04 0.02 3 0.04 0.03 0.02 0.01 Find Cov(X, Y). (Round the final answer to four decimal places. Include a minus sign if necessary.)
In a piston assembly, the specifications for the clearance between piston rings and the cylinder wall are very tight. In a lot of assemblies, let X be the number with too little clearance and let Y be the number with too much clearance. The joint probability mass function of X and Y is given in the table below: y x 0 1 2 3 0 0.15 0.12 0.11 0.10 1 0.09 0.07 0.05 0.04 2 0.06 0.05 0.04 0.02 3 0.04 0.03 0.02 0.01 Find the conditional probability mass function pY|X(y|1). (Round the final answer to two decimal places.) The value of pY|X(0|1) is . The value of pY|X(1|1) is . The value of pY|X(2|1) is . The value of pY|X(3|1) is Find the conditional probability mass function pX|Y(x∣2). pX|Y(0∣2) = (Round the final answer to one decimal place.) pX|Y(1|2) = (Round the final answer to four decimal places.) pX|Y(2|2) = (Round the final answer to four decimal places.) pX|Y(3|2) = (Round the final answer to four…
A box contains three cards, labeled 1, 2, and 3. Two cards are chosen at random, with the first card being replaced before the second card is drawn. Let X represent the number on the first card, and let Y represent the number on the second card. a) Find the joint probability mass function of X and Y. b) Find the marginal probability mass functions pX(x) and pY(y). c) Find µX and µY. d) Find µXY. e) Find Cov(X,Y).
A box contains three cards, labeled 1, 2, and 3. Two cards are chosen at random, with the first card being replaced before the second card is drawn. Let X represent the number on the first card, and let Y represent the number on the second card. Assume the first card is not replaced before the second card is drawn. a) Find the joint probability mass function of X and Y. b) Find the marginal probability mass functions pX(x) and pY(y). c) Find µX and µY. d) Find µXY. e) Find Cov(X,Y).
In a piston assembly, the specifications for the clearance between piston rings and the cylinder wall are very tight. In a lot of assemblies, let X be the number with too little clearance and let Y be the number with too much clearance. The total number of assemblies that fail to meet specifications is X + Y. The joint probability mass function of X and Y is given in the table below: y x 0 1 2 3 0 0.15 0.12 0.11 0.10 1 0.09 0.07 0.05 0.04 2 0.06 0.05 0.04 0.02 3 0.04 0.03 0.02 0.01 Find µX+Y. (Round the final answer to two decimal places.) Find σX+Y. (Round the final answer to four decimal places.) Find P(X + Y = 3). (Round the final answer to two decimal places.)
a. What value of c will make f(x) a valid probability mass function ?b. Compute P (1 < X < 6).
A survey of cars on a certain stretch of highway during morning commute hours showed that 70% had only one occupant, 15% had 2, 10% had 3, 3% had 4, and 2% had 5. Let X represent the number of occupants in a randomly chosen car. a) Find the probability mass function of X. b) Find P(X ≤ 2). c) Find P(X > 3). d) Find μX. e) Find σX.
Suppose that X and Y have a joint probability density function f(x,y)= 1, if0<y<1,y<x<2y; 0, otherwise. (a) Compute P(X + Y less than or equal 1). (b) Find the marginal probability density functions for X and Y , respectively. (c) Are X and Y independent?
Suppose that the random variables X,Y, and Z have the joint probability density function f(x,y,z) = 8xyz for 0<x<1, 0<y<1, and 0<z<1. Determine P(X<0.7).
Suppose that that joint probability mass function of X and Y is given in the following table. p(x,y) y 0 1 0 0.09 0.03 x 1 ? 0.17 2 0.13 0.09 Find the expected value of X.(Hint: First, find p(1,0). Then, you might want to find the (marginal) pdf of X).(Answer as a decimal number, and round to 2 decimal places).
Given a discrete RV X that takes on the values {-2, -1, 3, 4} and whose pmf (probability mass function) is: p-2 = 0.1 , p-1 = 0.2 , p3 = 0.6 , p 4 = 0.1 . Calculate the mean μ X of RV X.
Show that the following function satisfies the properties of a joint probability mass function. x y f XY ( x , y ) 1 1 1/4 1.5 2 1/8 1.5 3 1/4 2.5 4 1/4 3 5 1/8

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