Question

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

Answer #1

**A six sided die is rolled 10 times.**

**Number of times six is rolled, is recorded.**

**Now, six is rolled with probability 1/6, and non 6 is
rolled with chance 5/6.**

**So, the experiment has two outcomes, which are
complementary; so a six roll can be considered as success, and non
6 is considered as failure.**

**All the 10 rolls of the die, ie. all trials are
independent.**

**So, this is a binomial experiment.**

**If X be the random variable denoting the number of sixes
in these 10 rolls, then X follows binomial with parameters n = 10
and p = 1/6.**

**So, the given statement is TRUE.**

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...

Roll a single six-sided die 4 times and record the number of
sixes observed. Does the number of sixes rolled in 4 tosses of a
die meet the conditions required of a binomial random variable?
Construct the probability distribution for this experiment.

Example 1 A fair six-sided die is rolled six times. If the face
numbered k is the outcome on roll k for k=1, 2, ..., 6, we say that
a match has occurred. The experiment is called a success if at
least one match occurs during the six trials. Otherwise, the
experiment is called a failure. The sample space S={success,
failure} The event A happens when the match happens. A= {success}
Assign a value to P(A)
Simulate the experiment on...

If a single six-sided die is rolled five times, what is the
probability that a six is thrown exactly three times?
a)
0.125
b)
0.032
c)
0.042
d)
0.5

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(X2 − 4XY + Y2).

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:...

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].
Please solve it step by step especially the expectation
part. appreciate it.
You can draw some intuition graph and picture to help
you explain

You have a 4 sided die and 10 sided die that are rolled 50
times. What is the theoretical probability that the small die is
odd, the sum of the numbers is 5, the same # appears on both, the #
on the larger die is > than the # on the smaller die.

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) ????

A six-sided fair die is rolled six times independently. If side
i is observed on the ith roll, it is called a match on the ith
trial, i = 1, 2, 3, 4, 5, 6. Find the probabilities that
(a) all six trials result in matches,
(b) at least one match occurs in these six trials,
(c) exactly two matches occur in these six trials.

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