A single six-sided die, whose faces are numbered 1 to 6, is rolled n times. The...
Homework Answers
Given a fair six sided die is rolled "n" times.
Let X be the number of times that the number on the upward face of the die is 1.
The probability of getting number 1 on upward face in any trial is p=1/6
Therefore, 
Hence the mean of X is
The standard deviation of X is
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A
single six-sided die, whose faces are numbered 1 to 6, is rolled n
times. The...
Problem 1. Suppose that a fair six-sided die is rolled n times. Let N be the number of 1's rolled...
I know Pk~1/k^5/2 just need the
work
Problem 1. Suppose that a fair six-sided die is rolled n times. Let N be the number of 1's rolled, N2 be the number of 2's rolled, etc, so that NN2+Ns-n Since the dice rolls are independent then the random vector < N,, ,Ne > has a multinomial distribution, which you could look up in any probability textbook or on the web. If n 6k is a multiple of 6, let Pa be...
PLEASE SHOW EACH STEP- SHOW THE PROBABILITY WITH FRACTIONS A fair six-sided die has faces numbered...
PLEASE SHOW EACH STEP- SHOW THE PROBABILITY WITH FRACTIONS A fair six-sided die has faces numbered 1 through 6. A) What is the probability that the die would be rolled 3 times in order to get the first 2? B) What is the probability that the die would be rolled 4 times in order to get the first odd number?
5. A fair six sided die is rolled 10 times. Let X be the number of...
5. A fair six sided die is rolled 10 times. Let X be the number of times the number '6' is rolled. Find P(X2)
b) Find Var(X) 5. A fair six sided die is rolled 10 times. Let X be...
b) Find Var(X) 5. A fair six sided die is rolled 10 times. Let X be the number of times the number '6' is rolled. Find P(X2) B SEIKI
In this experiment, both a fair four-sided die and a fair six-sided die are rolled (these...
In this experiment, both a fair four-sided die and a fair six-sided die are rolled (these dice both have the numbers most people would expect on them). Let Z be a random variable that represents the absolute value of their difference. For instance, if a 4 and a 1 are rolled, the corresponding value of Z is 3. (a) What is the pmf of Z? (b) Draw a graph of the cdf of Z
A coin is tossed and a six-sided die numbered 1 through 6 is rolled
A coin is tossed and a six-sided die numbered 1 through 6 is rolled. Find the probability of tossing a head and then rolling a number greater than 2. The probability of tossing a head and then rolling a number greater than 2 is _______ (Round to three decimal places as needed.)
We roll a fair 8-sided die five times. (A fair 8-sided die is equally likely to...
We roll a fair 8-sided die five times. (A fair 8-sided die is equally likely to be 1, 2, 3, 4, 5, 6, 7, or 8.) (a) What is the probability that at least one of the rolls is a 3? (b) Let X be the number of different values rolled. For example, if the five rolls are 2, 3, 8, 8, 7, then X = 4 (since four different values were rolled: 2,3,7,8). Find E[X].
A fair (6-sided) die is rolled once, generating a number N. If the number N is...
A fair (6-sided) die is rolled once, generating a number N. If the number N is even, then a fair coin is tossed N + 1 times. If the number N is odd, then a fair coin is tossed 2N times. Let X be the number of heads obtained. Compute E(X). Give a numerical answer as a reduced fraction or a decimal expression accurate to at least 4 decimal places.
Three six-sided fair dice are rolled. The six sides are numbered 1,2,3,4,5,6. Let A be the...
Three six-sided fair dice are rolled. The six sides are numbered 1,2,3,4,5,6. Let A be the event that the first die shows an even number, let B be the event that the second die shows an even number, and let C be the event that the third die shows an even number. Express each of the following events in terms of the named events described above: 1) the event that all three dice show even numbers 2) the event that...
A fair die has the numbers 1, 2, 3, 4, 5, and 6 on its faces....
A fair die has the numbers 1, 2, 3, 4, 5, and 6 on its faces. Each face is equally likely to come up on a roll. You are conducting an experiment. You roll the die and record the number rolled. Then you roll the die again and add this second number to the first numbered rolled. The outcome of the experiment is this sum. List all of the possibilities for outcomes of this experiment?
I know Pk~1/k^5/2 just need the
work
Problem 1. Suppose that a fair six-sided die is rolled n times. Let N be the number of 1's rolled, N2 be the number of 2's rolled, etc, so that NN2+Ns-n Since the dice rolls are independent then the random vector < N,, ,Ne > has a multinomial distribution, which you could look up in any probability textbook or on the web. If n 6k is a multiple of 6, let Pa be...
5. A fair six sided die is rolled 10 times. Let X be the number of times the number '6' is rolled. Find P(X2)
b) Find Var(X) 5. A fair six sided die is rolled 10 times. Let X be the number of times the number '6' is rolled. Find P(X2) B SEIKI
We roll a fair 8-sided die five times. (A fair 8-sided die is equally likely to be 1, 2, 3, 4, 5, 6, 7, or 8.) (a) What is the probability that at least one of the rolls is a 3? (b) Let X be the number of different values rolled. For example, if the five rolls are 2, 3, 8, 8, 7, then X = 4 (since four different values were rolled: 2,3,7,8). Find E[X].
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