Question

A fair six-sided die is rolled 10 independent times. Let X be the number of ones and Y the number of twos.

(a) (3 pts) What is the joint pmf of X and Y?

(b) (3 pts) Find the conditional pmf of X, given Y = y.

(c) (3 pts) Given that X = 3, how is Y distributed conditionally?

(d) (3 pts) Determine E(Y |X = 3).

(e) (3 pts) Compute E(X^{2} − 4XY + Y^{2}).

Answer #1

I hope you'll understand the solution provided by me since it's step by step and conceptual.

Please do like it, and comment, if you've any more queries. Thanks.

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...

You roll a fair 6 sided die 5 times. Let Xi be the
number of times an i was rolled for i = 1, 2, . . . , 6.
(a) What is E[X1]?
(b) What is Cov(X1, X2)?
(c) Given that X1 = 2, what is the probability the
first roll is a 1?
(d) Given that X1 = 2, what is the conditional probability mass
function of, pX2|X1 (x2|2), of
X2?
(e) What is E[X2|X1]

A six-sided die is rolled 10 times and the number of times the
six is rolled is recorded. This is an example of a binomial
experiment.
Select one:
True
False

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

1) A 10-sided die is rolled infinitely many times. Let X be the
number of rolls up to and including the first roll that comes up 2.
What is Var(X)?
Answer: 90.0
2) A 14-sided die is rolled infinitely many times. Let X be the
sum of the first 75 rolls. What is Var(X)?
Answer: 1218.75
3) A 17-sided die is rolled infinitely many times. Let X be the
average of the first 61 die rolls. What is Var(X)?
Answer:...

Alice rolled a fair, six-sided die ten times and counted that
she got an even number six times.
Which of the following statements is FALSE?
The distribution of the count of getting an
odd number is binomial.
The distribution of the count of getting an
even number is binomial.
The distribution of the count of getting an
even number cannot be modeled as approximately normal if the die is
rolled more than 100 times.
The distribution...

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 pair of fair dice. Let X be the number of ones in the
outcome and let Y be the number of twos in the outcome. Are X and Y
independent?

A fair die is rolled three times. Let X denote the number of
different faces showing, X = 1, 2, 3. Find E(X). Give a good
explanation please

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 9 minutes ago

asked 19 minutes ago

asked 50 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago