Question

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.

Answer #1

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...

Consider a game where two 6-sided dice are rolled.
- Let X be the minimum of the two dice
- Let Y be the sum of the two dice
- Let Z be the first die minus the second die.
Write out the distributions of X, Y, and Z, respectively.

alex throws a fair tetrahedral die numbered 1,2,3 and 4 and an
octahedral (8-sided) die numbered 1,2,34,5,6,7,8. He defines M as
the product of is 2 numbers find;
a- p(M is odd)
b-p(M is prime)
c-P(M is both odd and prime)

Rihanna rolls a 4 sided fair die, then she selects at random,
without replacement, as many cards from the deck as the number
shown on the die. What is the probability that she gets at least
one Queen? (In your solution, define the corresponding events and
write down the given probabilities in terms of them. You do not
need to simply your final answer.)
Recall: There are 52 cards in a deck, 4 different suits (Clubs,
Spades, etc.) and 13...

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...

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

4 fair 10-sided dice are rolled.
(a)
Find the conditional probability that at least one die lands on
3 given that all 4 dice land on different numbers.
(b)
True or False: If X is the sum of the 4 numbers from
one roll, and Y is the maximum of the 4 numbers from one
roll, then X and Y are independent random
variables.

Troy is conducting an experiment. He first rolls a fair die
(six-sided) and then draw a chip out of a box containing 2 red
chips, 4 green chips, and 9 blue chips. What is the probability
Troy will roll a 3 and then draw a green chip?

You roll a fair 6-sided die once and observe the result which is
shown by the random variable X. At this point, you can stop and win
X dollars. Or, you can also choose to discard the X dollars you win
in the first roll, and roll the die for a second time to observe
the value Y. In this case, you will win Y dollars. Let W be the
number of dollars that you win in this game.
a)...

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...

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