Question

Roll a die twice and let Y be the sum of the two rolls. Find the...

Roll a die twice and let Y be the sum of the two rolls. Find the joint pmf of (X, Y ) if X is

(a) the number on the first roll

(b) the smallest number

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

if we carefully observe the outcomes you can understand the probability values obtained in both the pmfs.

probability is the number of outcomes that satisfy the condition given you the number of outcomes (36).

for example the sum should be 6 and first number x= 2 we have (2,4) combination which yields a sum of 6 with 2 as the number in the first roll. therefore p= 1/36.

the sum y=8 and smallest number of two rolls x= 3 we have (3,5) and (5,3) which yields sum as 8 therefore p=2/36 or 1/18

hope you understand any query please comment below thank you:)

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Roll a fair four-sided die twice. Let X be the sum of the two rolls, and...
Roll a fair four-sided die twice. Let X be the sum of the two rolls, and let Y be the larger of the two rolls (or the common value if a tie). a) Find E(X|Y = 4) b) Find the distribution of the random variable E(X|Y ) c) Find E(E(X|Y )). What does this represent? d) Find E(XY |Y = 4) e) Find the distribution of the random variable E(XY |Y ) f) Explain why E(XY |Y ) = Y...
A die is rolled six times. (a) Let X be the number the die obtained on...
A die is rolled six times. (a) Let X be the number the die obtained on the first roll. Find the mean and variance of X. (b) Let Y be the sum of the numbers obtained from the six rolls. Find the mean and the variance of Y
I roll a fair die until I get my first ace. Let X be the number...
I roll a fair die until I get my first ace. Let X be the number of rolls I need. You roll a fair die until you get your first ace. Let Y be the number of rolls you need. (a) Find P( X+Y = 8) HINT: Suppose you and I roll the same die, with me going first. In how many ways can it happen that X+Y = 8, and what is the probability of each of those ways?...
A 6-sided die rolled twice. Let E be the event "the first roll is a 1"...
A 6-sided die rolled twice. Let E be the event "the first roll is a 1" and F the event "the second roll is a 1". Find the probability of showing a 1 on both rolls. Write your answer as a reduced fraction.
8 Roll a fair (standard) die until a 6 is obtained and let Y be the...
8 Roll a fair (standard) die until a 6 is obtained and let Y be the total number of rolls until a 6 is obtained. Also, let X the number of 1s obtained before a 6 is rolled. (a) Find E(Y). (b) Argue that E(X | Y = y) = 1/5 (y − 1). [Hint: The word “Binomial” should be in your answer.] (c) Find E(X).
Alice rolls a six faced fair die twice, and she obtains two numbers that we denote...
Alice rolls a six faced fair die twice, and she obtains two numbers that we denote with X and Y , respectively. Fair die means that, in each roll, the six outcomes are equally likely. Let A be the event that X = 4, B be the event that X + Y = 6, and C be the event that Y = 5. (a) Write the sample space S for this experiment. (b) Are A and B independent? (c) Are...
Roll a die and let its outcome be the random variable X. Let Y be the...
Roll a die and let its outcome be the random variable X. Let Y be the random variable of “sum of X many dice rolled”. So, if X is 3, then we roll 3 dice and add the faces together to find Y . (a) Are X and Y independent? Explain. (b) Compute E[Y]
Roll a die and let its outcome be the random variable X. Let Y be the...
Roll a die and let its outcome be the random variable X. Let Y be the random variable of “sum of X many dice rolled”. So, if X is 3, then we roll 3 dice and add the faces together to find Y . (a) Are X and Y independent? Explain. (b) Compute E[Y]
Two identical fair 6-sided dice are rolled simultaneously. Each die that shows a number less than...
Two identical fair 6-sided dice are rolled simultaneously. Each die that shows a number less than or equal to 4 is rolled once again. Let X be the number of dice that show a number less than or equal to 4 on the first roll, and let Y be the total number of dice that show a number greater than 4 at the end. (a) Find the joint PMF of X and Y . (Show your final answer in a...
1) A 10-sided die is rolled infinitely many times. Let X be the number of rolls...
1) A 10-sided die is rolled infinitely many times. Let X be the number of rolls up to and including the first roll that comes up 2. What is Var(X)? Answer: 90.0 2) A 14-sided die is rolled infinitely many times. Let X be the sum of the first 75 rolls. What is Var(X)? Answer: 1218.75 3) A 17-sided die is rolled infinitely many times. Let X be the average of the first 61 die rolls. What is Var(X)? Answer:...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT