Question

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 E(X|Y )

g) Find E(E(XY |Y )). What does this represent?

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

Homework Answers

Answer #1

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 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
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.
Consider two rolls of a fair tetrahedral (4-sided) die. Calculate the PMF PZ(z) of a random...
Consider two rolls of a fair tetrahedral (4-sided) die. Calculate the PMF PZ(z) of a random variable Z = X + Y where X and Y are the random variables representing the result of the first and second rolls respectively.
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...
Suppose we roll a fair six-sided die and sum the values obtained on each roll, stopping...
Suppose we roll a fair six-sided die and sum the values obtained on each roll, stopping once our sum exceeds 376. Approximate the probability that at least 100 rolls are needed to get this sum. Probability =
Let X equal the outcome (1, 2 , 3 or 4) when a fair four-sided die...
Let X equal the outcome (1, 2 , 3 or 4) when a fair four-sided die is rolled; let Y equal the outcome (1, 2, 3, 4, 5 or 6) when a fair six-sided die is rolled. Let W=X+Y. a. What is the pdf of W? b What is E(W)?
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]
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?...
You roll two six-sided fair dice. a. Let A be the event that the first die...
You roll two six-sided fair dice. a. Let A be the event that the first die is even and the second is a 2, 3, 4 or 5. P(A) = Round your answer to four decimal places. b. Let B be the event that the sum of the two dice is a 7. P(B) = Round your answer to four decimal places. c. Are A and B mutually exclusive events? No, they are not Mutually Exclusive Yes, they are Mutually...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT