stat question and please explain, thank you A fair die is tossed two times independently: let...

stat question and please explain, thank you

A fair die is tossed two times independently: let W denote the product of the outcomes. Find the probability that W = 6.

Solutions

Expert Solution

For reference, see below table

Thank You!

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Suppose two fair sided die with sides labeled 1,2,3,4,5,6 are tossed independently. Let X = the...

Suppose two fair sided die with sides labeled 1,2,3,4,5,6 are tossed independently. Let X = the minimum of the value from each die. a. What is the probability mass function(pmf) of X? b. Find the mean E[X] and variance V (X). c. Write the cumulative distribution function (cdf) of X in a tabular form. d. Write F(x) the cdf of X as a step function and give a rough sketch for this function.

Q7 A fair coin is tossed three times independently: let X denote the number of heads...

Q7 A fair coin is tossed three times independently: let X denote the number of heads on the first toss (i.e., X = 1 if the first toss is a head; otherwise X = 0) and Y denote the total number of heads. Hint: first figure out the possible values of X and Y , then complete the table cell by cell. Marginalize the joint probability mass function of X and Y in the previous qusetion to get marginal PMF’s.

A die is rolled and, independently, a coin is tossed. Let X be the value of...

A die is rolled and, independently, a coin is tossed. Let X be the value of the die if the coin is H and minus the value of the die if the coin is T. (a) Calculate and plot the PMF of X. (b) Calculate E [X] and var(X) (c) Calculate and plot the PMF of X 2 − 2X. 2. A drunk walks down a street. Assume he starts at block 0. Every 10 minutes, he moves north a...

A fair coin is tossed, and a fair die is rolled. Let H be the event...

A fair coin is tossed, and a fair die is rolled. Let H be the event that the coin lands on heads, and let S be the event that the die lands on six. Find P(H or S).

Two fair six-sided dice are tossed independently. Let M = the maximum of the two tosses...

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) What is the pmf of M? [Hint: First determine p(1), then p(2), and so on.] (Enter your answers as fractions.) m 1 2 3 4 5 6 p(m) (b) Determine the cdf of M. (Enter your answers as fractions.)F(m) = m < 1 1 ≤ m <...

A fair die is tossed 120 times. A success is getting a 2 or a 5...

A fair die is tossed 120 times. A success is getting a 2 or a 5 landing face up. (a) Find the probability of getting exactly 40 successes. (b) Does the normal approximation to the binomial apply? If so, use it to approximate the probability of exactly 40 successes.

7. (Sec. 3.2) Two fair six-sided dice are tossed independently. Let M = the minimum of...

7. (Sec. 3.2) Two fair six-sided dice are tossed independently. Let M = the minimum of the two tosses. For example, M(2, 5) = 2, M(4, 4) = 4, etc. (a) What is the PMF of M? [Hint: just work out each probability individually by counting the number of outcomes which result in a specific value for M, i.e. find p(1), then p(2), and so on up to p(6)]. (b) Determine the CDF of M. ( c) Graph the CDF...

Two fair coins and a fair die are tossed. Find the sample space of the experiment...

Two fair coins and a fair die are tossed. Find the sample space of the experiment (10 pts); Find the probabilities of the following events: A- ”the die shows 2 or 3” (5 pts); B- ”one of the coins is head, the other - tail, and the die shows an odd number” (5 pts). Are the events A and B independent? (5 pts). Give proofs.

Two fair dice are tossed. Let A be the maximum of the two numbers and let...

Two fair dice are tossed. Let A be the maximum of the two numbers and let B be the absolute difference between the two numbers. Find the joint probability of A and B. Are A and B independent? How do you know?

A fair coin is tossed r times. Let Y be the number of heads in these...

A fair coin is tossed r times. Let Y be the number of heads in these r tosses. Assuming Y=y, we generate a Poisson random variable X with mean y. Find the variance of X. (Answer should be based on r).

Subjects