Question

a. Roll a dice, X=the number obtained. Calculate E(X), Var(X). Use two expressions to calculate variance.

b. Two fair dice are tossed, and the face on each die is observed. Y=sum of the numbers obtained in 2 rolls of a dice. Calculate E(Y), Var(Y).

c. Roll the dice 3 times, Z=sum of the numbers obtained in 3 rolls of a dice. Calculate E(Z), Var(Z) from the result of part a and b.

Answer #1

Answer:-

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

If you roll a die, you get one of the following numbers: 1, 2,
3, 4, 5, 6. Each possibility occurs with equal probability of 1/6.
The expected value of a dice roll is E(D)= 3.5 and the variance of
a dice roll is Var(X) = 2.917.
a) Suppose you roll a die and then add 1 to the roll to get a
new random variable taking one of the following numbers:
2,3,4,5,6,7. What is the variance of this new...

An actuary rolls two six-faced fair dice. The two numbers that
appear on the top face of the dice are observed. Calculate the
probability that the product of the two numbers is odd, given the
sum of the two numbers is between six and eight inclusive.

Consider rolling two fair six-sided dice.
a) Given that the roll resulted in sum of 8, find the
conditional probability that first die roll is 6.
b) Given that the roll resulted in sum of 4 or less, find the
conditional probability that doubles are rolled.
c) Given that the two dice land on different numbers, find the
conditional probability that at least one die is a 6.

Let’s assume that there are two dice, and we will roll one of
them, but we don’t know which one. The probability of rolling
either dice is 1/2. One of them is fair in the sense that all 6
outcomes are equally likely. The other die gives probability 1/3 to
numbers 1 through 3 and zero probability to numbers 4-6.
a-)The first roll was a 4. What is the probability that it was
the fair die?
b-)The first roll was...

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.

In a game, you roll two fair dice and observe the uppermost face
on each of the die. Let X1 be the number on the first die and X2 be
the number of the second die. Let Y = X1 - X2 denote your winnings
in dollars.
a. Find the probability distribution for Y .
b. Find the expected value for Y .
c. Refer to (b). Based on this result, does this seem like a
game you should play?

You roll a pair of fair dice repeatedly. Let X denote the number
of rolls until you get two consecutive sums of 8(roll two 8 in a
row). Find E[X]

Let X be the number showing when one true dice is thrown. Let Y
be the number of heads obtained when (2 ×X) true coins are then
tossed. Calculate E(Y) and Var(Y).

Hector will roll two fair, six-sided dice at the same time. Let
A = the event that at least one die lands with the number 3 facing
up. Let B = the event that the sum of the two dice is less than
5.
1. What is the correct set notation for the event that “at least
one die lands with 3 facing up and the sum of the two dice is less
than 5”? 2. Calculate the probability that...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 18 minutes ago

asked 29 minutes ago

asked 38 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago