Question

2 six-sided dice are thrown, Y is the random variable representing the product of the two dice.

What is the probability distribution p_{y}(k) and
cumulative distribution F_{y}(k). Using these, find the
expected product of the dice, E(Y).

Answer #1

Roll two six sided dice. Let Y be the random variable the
represents the product of the two dice.
Define W = 4Y + 2 and find E(W).

Two fair six-sided dice are rolled once. Let (X, Y) denote the
pair of outcomes of the two rolls.
a) Find the probability that the two rolls result in the same
outcomes.
b) Find the probability that the face of at least one of the
dice is 4.
c) Find the probability that the sum of the dice is greater than
6.
d) Given that X less than or equal to 4 find the probability
that Y > X.

Simultaneously roll two fair 3-sided dice whose sides are
numbered 1, 2, and 3. Let random variable K be the sum of the two
dice.
a) Calculate and plot the PMF of K.
b) Determine the expected value of K.
c) Calculate the variance of K.
d) Determine the expected value of K2 .
e) Determine the variance of K2 .

Rolling Snake Eyes
We roll two six-sided dice d1 and d2. What is
the probability that we roll two ones. (i.e., the probability that
d1=d2=1).
We roll two six-sided dice d1 and d2 and at
least one of the dice comes up as a one. What is the (conditional)
probability that we roll two ones.
We roll two six-sided dice d1 and d2 and at
least one of the dice comes up as a one. What is the (conditional)
probability...

1.) Two regular (six-sided) dice are thrown together. Use a tree
diagram to find the probability that one number is even and the
other is odd.
2.) The probability that January 1st of a randomly selected year
falls on a Monday is 1/7. The probability that January 1st and
January 8th of a randomly selected year both fall on a Monday is:
a.) 1/49 b.) 0 c.) 1 d.) 1/7 e.) 2/7
3.) In a group of 20 adults, there...

Four fair six sided dice are rolled. Given that at least two of
the dice land on an odd number, what is the probability that the
sum of the result of all four dice is equal to 14?

Suppose you roll two dice (normal six sided dice). What is the
probability that the sum of the spots on the up-faces is 4?

Suppose you roll two dice (normal six sided dice). What is the
probability that the sum of the spots on the up-faces is 4 or
8?

2. Let us define a new variable Y = the sum of two dice.
Complete both the probability and cumulative probability tables for
Y. (Hint: First think about what values Y can take on, and then
notice rolling a die produces 6 outcomes but rolling two dice
produces 36 outcomes. The following table can help you enumerate
all 36 outcomes and find out what is the associated Y value for
each outcome.) 1 2 3 4 5 6 1 Y=2...

You roll two dice. Let Y be a random variable that is the larger
of the two rolls (or, if the rolls are the same, your random
variable is that value).
Write Y as a function from the outcome space to the real
number
What is the distribution of Y?
What is P(Y≥5)?

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