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Problem 5. A lopsided six-sided die is rolled repeatedly, with each roll being independent. The probabil-...
(3.) A fair six-sided die is rolled repeatedly. Let R denote the random variable representing the...
(3.) A fair six-sided die is rolled repeatedly. Let R denote the random variable representing the outcome of any particular roll. The following random variables are all discrete-time Markov chains. Specify the transition probabilities for each (as a check, make sure the row sums equal 1) (a) Xn, which represents the largest number obtained by the nth roll. (b) Yn, which represents the number of sixes obtained in n rolls.
Suppose I asked you to roll a fair six-sided die 6 times. You have already rolled...
Suppose I asked you to roll a fair six-sided die 6 times. You have already rolled the die for 5 times and six has not appeared ones. Assuming die rolls are independent, what is the probability that you would get a six in the next roll? 1/6 1/2 5/6 0 1
Fair diced, which is unbiased. Each throw is independent. Step 1. You roll a six-sided die....
Fair diced, which is unbiased. Each throw is independent.
Step 1. You roll a six-sided die. Let X be the (random) number that you obtain. Step 2. You roll X six-sided dice. Let Y be the total number (sum) that you obtain from these X dice. Find E[Y], rounded to nearest .xx.
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...
dice is unbiased. Throws independent. Step 1. You roll a six-sided die. Let X be the...
dice is unbiased. Throws independent.
Step 1. You roll a six-sided die. Let X be the (random) number that you obtain. Step 2. You roll X six-sided dice. Let Y be the total number (sum) that you obtain from these X dice. Find E[Y] rounded to nearest .xx.
we repeatedly roll a fair 8-sided die six times and suppse X is the number of...
we repeatedly roll a fair 8-sided die six times and suppse X is the number of different values rolled. Find E[x] and E[Y]
A) Suppose I roll two fair six-sided dice. What is the probability that I rolled a...
A) Suppose I roll two fair six-sided dice. What is the probability that I rolled a total of 5? B) Suppose I roll two fair six-sided die and I announce that the sum of the two die is 6 or less. What is the probability that I rolled a total of 5?
1.) Suppose you roll two fair six-sided dice. What is the probabilty that I rolled a...
1.) Suppose you roll two fair six-sided dice. What is the probabilty that I rolled a total of 5? 2.) Suppose you roll two fair six-sided die and I announce that the sun of the two die is 6 or less. What is the probabilty that you rolled a total of 5?
A 6-sided die rolled twice. Let E be the event "the first roll is a 5"...
A 6-sided die rolled twice. Let E be the event "the first roll is a 5" and F F the event "the second roll is a 5". (a) Are the events E E and F F independent? Input Yes or No: (b) Find the probability of showing a 5 on both rolls. Write your answer as a reduced fraction. Answer:
you repeatedly roll an ordinary six sided die five times. Let X equal the number of...
you repeatedly roll an ordinary six sided die five times. Let X equal the number of times you roll the die. For example (1,1,2,3,4) then x =4 Find E[X]
(3.) A fair six-sided die is rolled repeatedly. Let R denote the random variable representing the outcome of any particular roll. The following random variables are all discrete-time Markov chains. Specify the transition probabilities for each (as a check, make sure the row sums equal 1) (a) Xn, which represents the largest number obtained by the nth roll. (b) Yn, which represents the number of sixes obtained in n rolls.
Fair diced, which is unbiased. Each throw is independent.
Step 1. You roll a six-sided die. Let X be the (random) number that you obtain. Step 2. You roll X six-sided dice. Let Y be the total number (sum) that you obtain from these X dice. Find E[Y], rounded to nearest .xx.
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...
dice is unbiased. Throws independent.
Step 1. You roll a six-sided die. Let X be the (random) number that you obtain. Step 2. You roll X six-sided dice. Let Y be the total number (sum) that you obtain from these X dice. Find E[Y] rounded to nearest .xx.
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