Two fair dice are rolled. Let X denote the smallest value of the two dice, and Y denote the product of the two dice.(a) Find fX,Y(x,y), fX(x), and fY(y) [you do not need to determine the mathematical function for these, it is fine to just list the probabilities].(b) Find prob(X=2|Y=12) and prob(Y=12|X=2).(c) Find E(Y|X=2). (d) Find Cov(X,Y).(e) Find Corr(X,Y).

Question
Asked Oct 31, 2019
302 views

Two fair dice are rolled. Let X denote the smallest value of the two dice, and Y denote the product of the two dice.

(a) Find fX,Y(x,y), fX(x), and fY(y) [you do not need to determine the mathematical function for these, it is fine to just list the probabilities].

(b) Find prob(X=2|Y=12) and prob(Y=12|X=2).

(c) Find E(Y|X=2). (d) Find Cov(X,Y).

(e) Find Corr(X,Y).

check_circle

Expert Answer

Step 1

Hello! As you have posted 5 sub parts, we are answering the first 3 sub-parts.  In case you require the unanswered parts also, kindly re-post that parts separately.

 

Step 2

(a).

 

From the given information, two fair dice are rolled.

 

help_outline

Image Transcriptionclose

(1.,1). (1,2).(13).(1,4). (1,5). (1,6) (2,1).(2,2).(2,3).(2,4). (2,5).(2,6) |(3,1).(3,2).(3,3),(3,4). (3,5) . (3, 6) (4,1).(4,2).(4,3).(4,4). (4,5) . (4, 6)| (5.1).(5,2).(5,3).(5.4). (5.5).(5,6) |(6,1).(6,2).(6,3).(6,4). (6,5) ,(6, 6)j

fullscreen
Step 3

Let us define the random variable X as smallest value of the two...

help_outline

Image Transcriptionclose

ух 1234 0 1 0 0 0 0 3 0 0 0 4 0 0 0 0 0 0 9 0 0 0 10 0 0 0 12 0 0 15 16 18 0 0 0 0 0 20 0 0 0 00 24 00 0 25 0 30 36 f) O Oo

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Probability

Related Probability Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: Let X1, X2, X3 and X4 be independent Unif(0, 1) distributed random variables (a) Compute P(X(3) X(4)...

A: (a) The value of P(X(3)+X(4)≤1) is 1 and it is obtained below: Let us consider, u= X(3)+X(4) and v= ...

question_answer

Q: A raffle ticket costs $5.  First and second prize winners will be drawn at random.  The probability ...

A: Let us assume 40 tickets sold, amount of one first prize is $100 and two second prize is $25. And 40...

question_answer

Q: Nine men and six women are to line up for a picture with the nine men in the middle. How many ways c...

A: It is provided that there are nine men and six women who are line-up for a picture with the nine men...

question_answer

Q: Consider the experiment of tossing a fair coin three times. Let X denote the number of heads on the ...

A: To determine the distribution functions for the random variables X and Y, as given

question_answer

Q: Probability of a author writing a good book isi The probability of the author publishing a good book...

A: From the given information,The probability of an author writing a good book is 1/2.The probability o...

question_answer

Q: A pediatrician wants to determine the relation that may exist between a child's height and head circ...

A: Part (a):In order to obtain the least square regression line, first perform regression analysis on t...

question_answer

Q: Phil Dunphy, a real estate agent, is considering whether he should list an unusual $372,875 house fo...

A: Expected value:The expected value of a random variable is the sum of the possible values that the ra...

question_answer

Q: Step 1 Exercise 29 gives a probability model for the grade of a randomly chosen student in Statistic...

A: If x represents values of the random variable  X and p(x) represents the corresponding probability t...

question_answer

Q: Answer the 2 parts of the question attached as images.

A: Note:Hey there! Thank you for posting the question. However, since there are multiple questions, acc...