1 Three-Card Monte Three cards labeled J, Q, and K are placed face-down on a table in a random order. We can think of this random experiment as having the sample space S = {JQK, JKQ, QJK, QKJ, KJQ, KQJ}. Let X be the random variable giving the position (1, 2, or 3) of the card Q on the table. (Note: to specify the various functions I ask you for in this problem, feel free to just list the input- output pairs in a form like "f(x1) = y₁, f(x2) = y2, ...") Write down X as a function from S to R. Give the range and probability mass function of X. If E is the event "Card J is not in position 3", give the range and probability mass function of X| E.
1 Three-Card Monte Three cards labeled J, Q, and K are placed face-down on a table in a random order. We can think of this random experiment as having the sample space S = {JQK, JKQ, QJK, QKJ, KJQ, KQJ}. Let X be the random variable giving the position (1, 2, or 3) of the card Q on the table. (Note: to specify the various functions I ask you for in this problem, feel free to just list the input- output pairs in a form like "f(x1) = y₁, f(x2) = y2, ...") Write down X as a function from S to R. Give the range and probability mass function of X. If E is the event "Card J is not in position 3", give the range and probability mass function of X| E.
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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Transcribed Image Text:1 Three-Card Monte
Three cards labeled J, Q, and K are placed face-down on a table in a random order. We can think
of this random experiment as having the sample space
S = {JQK, JKQ, QJK, QKJ, KJQ, KQJ}.
Let X be the random variable giving the position (1, 2, or 3) of the card Q on the table.
(Note: to specify the various functions I ask you for in this problem, feel free to just list the input-
output pairs in a form like "f(x1) = y₁, f(x2) = y2, ...")
Write down X as a function from S to R.
Give the range and probability mass function of X.
If E is the event "Card J is not in position 3", give the range and probability mass
function of X| E.
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