5. Find the expected value of the sum obtained when n fair six-sided dice are tossed.
5. Find the expected value of the sum obtained when n fair six-sided dice are tossed.
2. Two fair six-sided dice are tossed independently. Let M = the maximum of the two tosses (so M (1,5) = 5, M (3,3) = 3, etc). (a) I4 ptsl Find the probability mass function of M. (b) 14 pts] Find the cumulative distribution function of M and graph it. (c) 12 pts] Find the expected value of M (d) 12 pts] Find the variance of M. (e) 12 pts] Find the standard deviation of M.
If two standard six sided dice are tossed and if the dice equal the sum of 2 you win 1000 dollars but if it lands on anything else you lose 100 dollars what are the probabilities that u win 1000 and how many trails would you need or expect to win on average and is it worth the risk and why
If you roll two fair six-sided dice, what is the probability that the sum is 4 or higher?
If you roll two fair six-sided dice, what is the probability that the sum is 4 or higher?
A standard six sided dice is tossed repeatedly. Let N be the total number of observed 1s and 2s. For independent individual outcomes, calculate p(N=infinity) (Hint continuity) Full solution with justification.
Suppose that you roll 112 fair six-sided dice. Find the probability that the sum of the dice is less than 400. (Round your answers to four decimal places.)You may need to use the appropriate table in the Appendix of Tables to answer this question.
Suppose that five 9-sided dice are tossed. What is the probability that the sum on the five dice is greater than or equal to 7?
1. Suppose a fair six-sided die is tossed, with N being the resulting number on the uppermost face. Given N, a fair coin is tossed independently until N heads are recorded. Let X be the total number of tails recorded. a. What is the pmf of N? (5 pts) b. Given N = 3, what is the distribution of X? (10 pts) c. What is Pr(X = 1)? (10 pts) d. What is E(X)? (10 pts)
Let S(sub k) denote the event that the sum of three fair typical six-sided dice is k. Assume that one die is red, one is green and one is blue so that the three dice are distinguishable. Compute P(S(sub k), for all values of k.
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?