Question

In: Statistics and Probability

Two fair dice are rolled. Let X be the product of the number of dots that...

Two fair dice are rolled. Let X be the product of the number of dots that show up.
(a) Compute P(X = n) for all possible values of n.
(b) Compute E(X).
(c) Compute Var(X) and SD(X).

Solutions

Expert Solution


Related Solutions

Two fair dice are rolled at once. Let x denote the difference in the number of...
Two fair dice are rolled at once. Let x denote the difference in the number of dots that appear on the top faces of the two dice. For example, if a 1 and a 5 are rolled, the difference is 5−1=4, so x=4. If two sixes are rolled, 6−6=0, so x=0. Construct the probability distribution for x. Arrange x in increasing order and write the probabilities P(x) as simplified fractions.
Suppose two fair dice are rolled. Let X denote the product of the values on the...
Suppose two fair dice are rolled. Let X denote the product of the values on the dice and Y denote minimum of the two dice. Find E[X] and E[Y] Find Var X and Var Y Let Z=XY. Find E[Z]. Find Cov(X,Y) and Corr(X,Y) Find E[X|Y=1] and E[Y|X=1]
2. Three fair dice are rolled. Let X be the sum of the 3 dice. (a)...
2. Three fair dice are rolled. Let X be the sum of the 3 dice. (a) What is the range of values that X can have? (b) Find the probabilities of the values occuring in part (a); that is, P(X = k) for each k in part (a). (Make a table.) 3. Let X denote the difference between the number of heads and the number of tails obtained when a coin is tossed n times. (a) What are the possible...
two fair dice are each rolled once. Let X denote the absolute value of the difference...
two fair dice are each rolled once. Let X denote the absolute value of the difference between the two numbers that appear. List all possible values of X Find the probability distribution of X. Find the probabilities P(2<X<5) and P(2£X<5). Find the expected value mand standard deviation of X.
Two fair dice are rolled: a) What is the probability of an even number or a...
Two fair dice are rolled: a) What is the probability of an even number or a 3 on the first die? Are these two events mutually exclusive and why? b) What is the probability of an even number on the first die and a 5 on the second? Is conditional probability involved in this case? Why or why not?
Three fair dice are rolled. Let S be the total number of spots showing, that is...
Three fair dice are rolled. Let S be the total number of spots showing, that is the sum of the results of the three rolls. a) Find the probabilities P(S = 3), P(S = 4), P(S = 17), P(S = 18). b) Find the probability P(S ≥ 11).
Two dice are rolled. Let the random variable X denote the number that falls uppermost on...
Two dice are rolled. Let the random variable X denote the number that falls uppermost on the first die and let Y denote the number that falls uppermost on the second die. (a) Find the probability distributions of X and Y. x 1 2 3 4 5 6 P(X = x) y 1 2 3 4 5 6 P(Y = y) (b) Find the probability distribution of X + Y. x + y 2 3 4 5 6 7 P(X...
Two fair dice are thrown. Let X be the number of 5’s and Y be the...
Two fair dice are thrown. Let X be the number of 5’s and Y be the number of 6’s. Find (a) the joint PMF of X and Y, (b) the two marginal distributions (PMFs), and (c) the conditional distribution (PMF) of Y given X = x for each possible value of X.
1. Suppose that two fair dice are rolled. Find the probability that the number on the...
1. Suppose that two fair dice are rolled. Find the probability that the number on the first die is a 6 or the number on the second die is a 2.
2 dice are rolled. Let X be the number on the first die, Y - on...
2 dice are rolled. Let X be the number on the first die, Y - on the second, and Z=X - Y. Find the expectation and standard deviation of Z.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT