Question

Roll a die 8 times. Compute the probability that a number occurs
6 times and two other

numbers occur 1 time each.

Answer #1

A loaded 8-sided die is loaded so that the number 4 occurs 3/10
of the time while the other numbers occur with equal frequency.
What is the expected value of this die?

Roll a die 10 times. Put a 1 each time
the die is a one and a 0 each time the die comes up any other
number. Count the number of ones you obtained and divide by 10.
a. What number did you get? This is
your estimate of the probability of obtaining a one.
b. Is the number you obtained in part
(a) a parameter or a statistic?
c. Now roll the die 25 times. Put a 1
each...

if you roll a fair die 7 times, find the probability that you
never roll a number smaller than 6

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]

You roll a fair die 5 times. What is the probability you get at
least four 6’s? This time you roll the die 204 times. What is the
probability you get between 30 and 40 6’s?

Roll one die 100 times:
What is the probability that the average number face-up is
a) 1
b) 2
c) 3
d) 4
e) 5
g) 6
Could you please calculate the following probabilites and
explain how?

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...

Suppose you plan to roll a fair six-sided die two times. What is
the probability of rolling a ‘1’ both times?
Group of answer choices

Suppose that we roll a die 247 times. What is the approximate
probability that the sum of the numbers obtained is between 829 and
893, inclusive.

Suppose that we roll a die 208 times. What is the approximate
probability that the sum of the numbers obtained is between 685 and
775, inclusive.

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