Question

Two standard six-sides dices are rolled once. Let the random
variable X be the sum of the numbers. List all the values of the
pmf of X

Answer #1

Two standard six-sided dices are rolled. Find the probability
that the numbers are 2 and 4 under the condition that the sum of
the numbers is 6.

Let X be a rv equal to the sum of two rolled die. Define the
elements of the sample space of X and calculate f(x) (the PMF) and
F(x) (the CDF) for X.

If two fair dices are rolled, find the probabilities of the
following;
a) A sum of 8 or a double(like 1−1,2−2, ect) ?

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.

A fair die is rolled repeatedly. Let X be the random variable
for the number of times a fair die is rolled before a six appears.
Find E[X].

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

Consider the experiment of tossing two dices. Let X denote the
total of the upturned faces.
a. Calculate the pmf f(x) and cdf F(x) of X.
b. Calculate Q(p) such that p = 0.20, 0.50, and 0.75.

A fair six-sided die has two sides painted red, 3 sides painted
blue and one side painted yellow.
The die is rolled and the color of the
top side is recorded.
List all possible outcomes of this random experiment
Are the outcomes equally likely? Explain
Make a probability distribution table for the random variable
X: color of the top side
2. If a pair of dice painted the same way as in problem 1 is
rolled, find the probability...

A dice is rolled once. The random variable X is defined to be 1
if the outcome is 1 or 3,
to be 2 if the outcome is 2 or 4, and to be 3 if the outcomes is 5
or 6.
a) Find fx(x) and Fx(x)
b) Find fx(x/M) and Fx(x/M) if
the event M is outcome to be even, M = {2,4,6}.

A novelty die with six sides is printed with the numbers 1, 2,
3, 4, 8, 16. (a) If the die is rolled once what is the probability
of geting an odd number? (b) If the die is rolled twice and the
numbers for each roll added together, what is the probability of
getting an odd sum?

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