1. Consider the following random experiment: there is a bag with 4 marbles in it, two red and two blue. We draw two marbles from the bag, without replacement. To make the sampling uniform, let's label the two red marbles R₁ and R2 and the two blue marbles B₁ and B₂. Then the sample space is {R₁ R2, R₁B₁, R₁B2, R₂B₁, R2B2, B₁B2}. Finally, let X be the indicator variable equal to 1 if the two marbles drawn have the same color, and 0 if they have different colors. (a) Write down X as a function from the sample space to the real numbers. (b) What is Rx, the range of X? (c) Write down the probability mass function Px of X: this is a function from the range of X to the interval [0, 1].
1. Consider the following random experiment: there is a bag with 4 marbles in it, two red and two blue. We draw two marbles from the bag, without replacement. To make the sampling uniform, let's label the two red marbles R₁ and R2 and the two blue marbles B₁ and B₂. Then the sample space is {R₁ R2, R₁B₁, R₁B2, R₂B₁, R2B2, B₁B2}. Finally, let X be the indicator variable equal to 1 if the two marbles drawn have the same color, and 0 if they have different colors. (a) Write down X as a function from the sample space to the real numbers. (b) What is Rx, the range of X? (c) Write down the probability mass function Px of X: this is a function from the range of X to the interval [0, 1].
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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![1. Consider the following random experiment: there is a bag with 4 marbles in it, two red and
two blue. We draw two marbles from the bag, without replacement.
To make the sampling uniform, let's label the two red marbles R₁ and R2 and the two blue
marbles B₁ and B2. Then the sample space is
{R₁R2, R₁B₁, R₁B2, R2B1, R2B2, B1B2}.
Finally, let X be the indicator variable equal to 1 if the two marbles drawn have the same
color, and 0 if they have different colors.
(a) Write down X as a function from the sample space to the real numbers.
(b) What is Rx, the range of X?
(c) Write down the probability mass function Px of X: this is a function from the range of
X to the interval [0, 1].
(d) Identify the distribution of X by name, and give the parameter(s) of that distribution.
(The functions in parts (a) and (c) of this problem both have only finitely many possible
inputs. I don't care what notation you use in your answer, as long as you give me the value
of the function for every possible input.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F232028c3-8426-43ce-b04a-a507a5240356%2Fd38a1605-abcf-43e6-bb2d-6e8326243390%2F3sj8vti.jpeg&w=3840&q=75)
Transcribed Image Text:1. Consider the following random experiment: there is a bag with 4 marbles in it, two red and
two blue. We draw two marbles from the bag, without replacement.
To make the sampling uniform, let's label the two red marbles R₁ and R2 and the two blue
marbles B₁ and B2. Then the sample space is
{R₁R2, R₁B₁, R₁B2, R2B1, R2B2, B1B2}.
Finally, let X be the indicator variable equal to 1 if the two marbles drawn have the same
color, and 0 if they have different colors.
(a) Write down X as a function from the sample space to the real numbers.
(b) What is Rx, the range of X?
(c) Write down the probability mass function Px of X: this is a function from the range of
X to the interval [0, 1].
(d) Identify the distribution of X by name, and give the parameter(s) of that distribution.
(The functions in parts (a) and (c) of this problem both have only finitely many possible
inputs. I don't care what notation you use in your answer, as long as you give me the value
of the function for every possible input.)
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