Question

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 time the die comes up as a one and a 0 for any other number. Count the number of ones you obtained and divide by 25. What number did you get?

d. What is the chance you obtain a one with a fair die? How do you believe this number is obtained using your results from parts (a) and (c)?

e. How does this process relate to the idea of a sampling distribution?

Answer #1

a) The die is rolled 10 times and the number'1' is obtained 2
times.

The number obtained is 2/10 = 0.20. This is the estimate of
probability of obtaining a one.

b) The number obtained is a statistic as it is obtained from a sample of 10 trials.

c) The die is rolled 25 times. The number '1' comes up 4 times. The number obtained is 4/25 = 0.16

d) The chance of obtaining a one with a fair die = 1/6 =
0.167

We are getting closer and closer to the desired value as the number
of trials increases. Hence, through parts a) and c) we have reached
closer to the result.

e) The process related to the idea of a sampling distribution as it follows the law of large numbers. As the number of trials or sample size increases, the statistic obtained converges to the desired value or parameter.

Roll a die 8 times. Compute the probability that a number occurs
6 times and two other
numbers occur 1 time each.

Make a box model for the following problem:
You roll a die 5 times. For each time you roll the die, you win
$5 if you roll a 1. You win $10 if you roll a 2. Otherwise, you
lose $1.

If you roll a 4-sided die and a 6-sided die at the same time and
then add the result on each of the dice, how many different ways
can you get a number greater than 7?

There are six normal dice in a box, and one special die (which
has sixes on two sides and ones on the remaining four sides). We
randomly draw a die, and then roll it 10 times.
a) What is the probability that each number obtained will be a 1
or a 6?
b) What is the probability that we have chosen the special die,
given that each number obtained was a 1 or a 6?

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?

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:...

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...

(3) For the random experiment “roll a balanced die 3 times”,
what’s the total count of the sample space? What are the chances
that the three numbers add up to 5? What are the chances that there
are two even numbers and one odd number among the 3 rolls? What are
the chances that there are more even numbers than odd numbers among
the 3 rolls?

You are playing another dice game where you roll just one
die--this time, you lose a point if you roll a 1. You are
going to roll the die 60 times. Use that information to answer the
remaining questions.
A. What are the values of p and q? (Hint: notice this is
binomial data, where p is the probability of losing a point and q
is the probability of not losing a point.) p =
and q =
B....

1: How many possible outcomes are there if you 3 times in a row
either roll a die or flip a coin each time?
2: How many different outcomes are there if 3 numbers are drawn
in sequence out of a bucket containing the numbers 0 -9?
3: How many possibilities are there for 3 consecutive rolls of a
die without two consecutive rolls leading to the same number ?

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