Suppose that a fair die is rolled n times. We say that there is a repeat at the i’th place if the...
Suppose that a fair die is rolled n times. We say that there is a repeat at the i’th place if the same number occurs on both the i’th and i + 1’st roll. Let X be a random variable representing the number of repeats. Find E[X].
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Any query then comment below...i will ecplain you...
Understand carefully...
We take an exple to understand this...
Let we throw 3 times okk..
And repeat at 1st place means we have 1st and 2nd entry same....
So , means on first and secone place we have (1,1) , (2,2) ..... (6,6) ...ok....and 3rd place we have 6 choices...so we have probability is (6*6)/216 = 36/216 = 1/6 ...
Same think happen in n also...
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Suppose that a fair die is rolled n times. We say that there is a repeat at the i’th place if the...
Suppose that a fair die is rolled n times. We say that there is an increase at the i’th place if ...
Suppose that a fair die is rolled n times. We say that there is an increase at the i’th place if result on the i + 1’st roll is greater than the result on the i’th roll. Let X be a random variable representing the number of increases. Find E[X].
Suppose that a fair die is rolled n times. We say that there is an increase...
Suppose that a fair die is rolled n times. We say that there is an increase at the i’th place if result on the i + 1’st roll is greater than the result on the i’th roll. Let X be a random variable representing the number of increases. Find E[X].
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...
7. In n rolls of a fair die, let X be the number of times 1 is rolled, and Y the number of times ...
7. In n rolls of a fair die, let X be the number of times 1 is rolled, and Y the number of times 2 is rolled. Find the conditional distribution of X given Y-m
7. In n rolls of a fair die, let X be the number of times 1 is rolled, and Y the number of times 2 is rolled. Find the conditional distribution of X given Y-m
A single six-sided die, whose faces are numbered 1 to 6, is rolled n times. The...
A single six-sided die, whose faces are numbered 1 to 6, is rolled n times. The die is fair, each face is equally likely to land upward when the die is rolled. Let X be the number of times that the number on the upward face of the die is 1. Find the mean and the standard deviation of the random variable X.
A fair die is rolled three times. We say that a match has occurred if the outcome of the first throw is 2, or the outcom...
A fair die is rolled three times. We say that a match has occurred if the outcome of the first throw is 2, or the outcome of the second throw is 2, or the outcome of the third throw is 3. Find the probability of the event that a match occurs.
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].
1. Roll the die 40 times and record the rolled values in the table below. These...
1. Roll the die 40 times and record the rolled values in the table below. These represent 40 observations of X. 2. Calculate the sample mean of your 40 rolls using Excel. This number represents a single observation of the random variable X (which, again, is a random variable representing the sample mean of 40 rolls of a die). Record the value for the sample mean in the space below: Sample Mean Observation (= first observation of X): 4. Do...
(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.
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]
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...
7. In n rolls of a fair die, let X be the number of times 1 is rolled, and Y the number of times 2 is rolled. Find the conditional distribution of X given Y-m
7. In n rolls of a fair die, let X be the number of times 1 is rolled, and Y the number of times 2 is rolled. Find the conditional distribution of X given Y-m
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].
1. Roll the die 40 times and record the rolled values in the table below. These represent 40 observations of X. 2. Calculate the sample mean of your 40 rolls using Excel. This number represents a single observation of the random variable X (which, again, is a random variable representing the sample mean of 40 rolls of a die). Record the value for the sample mean in the space below: Sample Mean Observation (= first observation of X): 4. Do...
(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.
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