Skip to main content

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
100%

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).

Expert Solution

Want to see the full answer?

Check out a sample Q&A here
Blurred answer
Students who’ve seen this question also like:
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN: 9781305658004
Author: Ron Larson
Publisher: Cengage Learning
Not helpful? See similar books
Learn more about
Continuous Probability Distrib...
marketing sidebar icon
Want to see this answer and more?
Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*
*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.

Related Probability Q&A

Find answers to questions asked by students like you.

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= ...

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...

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...

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

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...

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...

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...

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...

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...

Q: Section 6.1 Summarizi 62 Dental Insurance You plan to purchase dental insurance for your three remai...

A: As per the questiona) X = payout of dental insurance is a random variable because it takes different...

Q: The table shows data collected on the relationship between the average daily temperature and time sp...

A: Given dataLine of best fit

Q: Two fair distinct dice are tossed. What is the probability of getting a 6 or a 7 in a toss of two di...

A: Note:Hi there! Thank you for posting the question. Since getting a 7 in a toss is impossible, we ass...

Q: 4. A population has a normal distribution with a mean of 32.9 and a standard deviation of 35.2. Draw...

A: From the given information mean and standard deviations are 32.9 and 35.2

Q: You draw two cards from a standard deck of 52 cards without replacing the first one before drawing t...

A: (a) From the given information, two cards are selected from the deck of 52 cards without replacing t...

Q: Can you please answer this question and show the steps

A: Concept of General Addition Rule:For any two events A and B the General Addition Rule state that:

Q: The Textbook answer to 3.7.45 is 1/12 however I dont understand how

A: To compute the required probability

Q: A manufacturer buys 30% of a certain part from one supplier and 70% from a second supplier. If 2% of...

A: Introduction:Let A be the event that a randomly selected part is from the first supplier; so, AC den...

Q: from 1 draw, find, (deck of cards) (a) P(diamonds) (b) P( King of diamonds)

A: There are 52 cards in a standard deck of cards in which 13 are diamonds.

Q: alow.P many ways can they sit in a row if the boys and girls are each to sit together? (c) In how ma...

A: We have 4 identical red flags and 2 identical blue flags. We need to find that how many different si...

Q: The weight of topsoil sold in a week is normally distributed with a mean of 2000 tons and a standard...

A: (a)The percentage of weeks will sales exceed 2100 tons is,

Q: 10. a.) Find the z-value such that 80 percent of the area under the standard normal curve lies betwe...

A: Click to see the answer

Q: A president, vice president, and 2 at-large members are selected for a school council from 10 people...

A: Combination:It represents the number of ways to choose x elements from a set of n elements. In combi...

Q: Assume that different groups of couples use a particular method of gender selection and each couple ...

A: a.Let X is random variable denotes the number of girls’ birth follows the binomial distribution.The ...

Q: 5.32 Cancer deaths Current estimates are that about 25% of all deaths are due to cancer, and of the ...

A: Multiplication Rule:Multiplication rule for two dependent events C and D is given by:

Q: Suppose you have 3 jars with the following contents. Jar 1 has 1 white ball and 1 black ball. Jar 2 ...

A: Consider,J1 be the jar one that has 1 white ball and 1 black ball.J2 be the jar two that has 2 white...

Q: A spinner game has a wheel with the numbers 1 through 21 marked in equally spaced slots. You pay $1 ...

A: From the given information, a spinner game has a wheel with numbers 1 to 21 marked with equally spac...

Q: Assume that you have a total of 15 people on the board: 5 out-of-state seniors, 4 in-state seniors, ...

A: Number of ways can the officers be chosen while still conforming to university rules is obtained bel...

Q: The numbers 7, 8, 9, and 11 are written on separate pieces of paper and put into a hat. Two pieces o...

A: Sample space: the sample space is an experiment of random trial is the set of all possible outcomes ...

Q: Brandybuck Insurance Company (BIC) is deciding whether to insure the lives of those leading a quest ...

A: Given data

Q: (Fill in the blank below and give your answer as a whole number.) 1 chance of winning $600(with a- 9...

A: The mean payoff is,

Q: Step 1: License plates in Florida have the form A12BCD, that is, a letter followed by two digits fol...

A: Form of License plates A12BCD Total alphabetical letters are 26 A-ZTotal numerical are 0- 9

Q: A die is rolled, and two coins are flipped. The number on the die is doubled for each tail that come...

A: As per the question, all the possible outcomes are shown in the table

Q: 5. A random sample of size 2, Yi and Y2 is drawn from the pdf fr (y; 0)323,0 < y < What must c equal...

A: From the given information,The sample size 2 that is Y1 and Y2 is drawn from the given density funct...

Q: A Bernoulli process has 4 trials and probability of success 0.31. Find the following probabilities. ...

A: The number of Bernoulli trials, n is 4 and the probability of success, p is 0.31.1.The number of fai...

Q: A standard 5-card poker hand is drawn simultaneously from a deck of 52 cards. You draw a “flush” if ...

A: Introduction:The probability of an event in an experiment is the number outcomes in the experiment t...

Q: How do you find the correct probability for something such as finding a green bead among red beads (...

A: The question is regarding selecting a green bead from a collection which consists of beads of two co...

Q: Assume that the box contains balls numbered from 1 through 26, and that 3 are selected. A random var...

A: As per the question, the number can be either odd or even and 3 are selectedSo total possible combin...

Q: Assume that random guesses are made for thirteen multiple choice questions on a medical admissions​ ...

A: Introduction:If X ~ Bin (n, p), then the probability mass function of X is:p (x) = (nCx) px (1 – p)n...

Q: A fan of country music plans to make a custom CD with 12 of her 25 favorite songs. How many differen...

A: Given dataTotal songs N = 25 No of combinations for size 12 is given by

Q: While taking a walk along the road where you live, you accidentally drop your glove, but you don't k...

A: The PDF for having dropped the glove x kilometers from home is given by,

Q: Show that: (a) Cov(X,Y) = E[XY] – E[X]E[Y]. (b) If X and Y are independent, then fY|X(y|x) = fY(y)

A: Solution:a.Show that COV(X,Y)=E(XY)–E(X)E(Y)

Q: We learned in class that when dealing with small samples, we use df = n-1 to calculate the sample st...

A: To calculate standard deviation , we use sample mean value or population mean value depending on the...

Q: An experiment consists of casting a pair of fair six sided dice (one green and one red) and observin...

A: Hey, since multiple sub parts are posted, we will answer first three subparts according to our polic...

Q: If P(B) = 0.3, P(A or B)= .06, and P(A and B)= .2, find P(A)

A: From the properties of probability, for any two events A and B we have

Q: in the attached, I only need help with the last three parts. E, G, and H thanks

A: According to the provided data, the square footage is the explanatory variable and selling price is ...

Q: A sample of 200 students at a Big-Ten university was taken after the midterm to ask them whether the...

A: Introduction:The sample proportion is a good estimator of the population proportion, if the sample i...

Q: The following data represent the flight time (in minutes) of a random sample of seven flights from o...

A: Range:In a data set, the difference between the maximum value and minimum value is called range.Samp...

Q: The percent of defects is the x-coordinate, while the percent of new machines is the y-coordinate. S...

A: Using the information given in the question and make a table: 

Q: A beverage plant has three lines (line A, line B and line C) for bottling the beverages. Line A bott...

A: Let A be the event of selecting line A, B be the event of sleeting line B and C be the event of sele...

Q: A biomedical research company produces 40%40% of its insulin at a plant in Kansas City, and the rema...

A: Click to see the answer

Knowledge Booster
Probability
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.
Recommended textbooks for you
  • Elementary Linear Algebra (MindTap Course List)
    Algebra
    ISBN:9781305658004
    Author:Ron Larson
    Publisher:Cengage Learning
    College Algebra
    Algebra
    ISBN:9781305115545
    Author:James Stewart, Lothar Redlin, Saleem Watson
    Publisher:Cengage Learning
    Algebra and Trigonometry (MindTap Course List)
    Algebra
    ISBN:9781305071742
    Author:James Stewart, Lothar Redlin, Saleem Watson
    Publisher:Cengage Learning
  • Elementary Linear Algebra (MindTap Course List)
    Algebra
    ISBN:9781305658004
    Author:Ron Larson
    Publisher:Cengage Learning
    College Algebra
    Algebra
    ISBN:9781305115545
    Author:James Stewart, Lothar Redlin, Saleem Watson
    Publisher:Cengage Learning
    Algebra and Trigonometry (MindTap Course List)
    Algebra
    ISBN:9781305071742
    Author:James Stewart, Lothar Redlin, Saleem Watson
    Publisher:Cengage Learning