Question

QUESTION 8

Die Question 1

A regular, i.e., six-faced and balanced, die will be rolled
twice. Let the random variable X be equal to the result of
subtracting the number obtained on the second roll from the number
obtained on the first roll.

Find P open parentheses X less or equal than 3 close
parentheses .

a.

0.8889

b.

0.8611

c.

0.9167

d.

0.8333

e.

0.8588

Answer #1

QUESTION 9
Die Question 2
A regular, i.e., six-faced and balanced, die will be rolled
twice. Let the random variable X be equal to the result of
subtracting the number obtained on the second roll from the number
obtained on the first roll.
Find the variance of X.
a.
2.9167
b.
5.8333
c.
8.75
d.
11.6667
e.
none of the above

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

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...

A 6-sided die rolled twice. Let E be the event "the first roll
is a 1" and F the event "the second roll is a 1".
Find the probability of showing a 1 on both rolls. Write your
answer as a reduced fraction.

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 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?

A balanced die with six sides is rolled 60times. X=number of
6s.
If you observe x=0, would you be skeptical that the dice is
balanced? Explain why, based on the mean and standard deviation of
X.
I already looked for the answers, but there are different
opinions and I can't understanding what it is correct. I don't want
to know a trivial solution.
60times rolling is pretty large and the binomial distribution
will follow the Normal distribution. After calculating the...

A six-sided die is rolled, and the number N on the uppermost
face is recorded. From a jar containing 10 tags numbered 1,2,...,10
we then select N tags at random without replacement. Let X be the
smallest number on the drawn tags. Determine Pr{X=2}and E[X].
for this question, i really want to know why i cant use
P(X|N)=P(X=x,N=n)/P(N=n) ????

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...

PROBLEM #2
Suppose you play a game in which a fair 6 sided die is rolled
once. If the outcome of the roll (the number of dots on the side
facing upward) is less than or equal to 4, you are paid as many
dollars as the number you have rolled. Otherwise, you lose as many
dollars as the number you have rolled.
Let X be the profit from the game (or the amount of money won or
lost per...

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