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]
we repeatedly roll a fair 8-sided die six times and suppse X is the number of...
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].
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]
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)
problem 4 you repeatedly roll an ordinary eight-sided die five times. Let X equal the number of times you roll the die. Let Y equal the value of the first roll What is E[x] and E[Y]
Problem 5. A lopsided six-sided die is rolled repeatedly, with each roll being independent. The probabil- ity of rolling the value i is Pi, i = 1, … ,6. Let Xn denote the number of distinct values that appear in n rolls. (a) Find E|X, and E21 (b) What is the probability that in the n rolls of the dice, for n 2 3, a 1, 2, and 3 are each rolled at least once?
We roll a fair die repeatedly. Let N be the number of rolls needed to see the first six, and let Y be the number of fives in the first N -1 rolls. In class, we saw that E[Y I N]- (N - 1)/5. Using this, find EiY]. Also, find Cov(Y, N). Hint: N -1 is a geometric random variable. (Why?)
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
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
6. A fair six sided die is rolled three times. Find the probability that () all three rolls are either 5 or 6 (6) all three rolls are even (c) no rolls are 5 (d) at least one roll is 5 (e) the first roll is 3, the second roll is 5 and the third roll is even
(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.