# Question: Let X equal the outcome when a fair four sided die

Let X equal the outcome when a fair four-sided die that has its faces numbered 0, 1, 2, and 3 is rolled. Let Y equal the outcome when a fair four-sided die that has its faces numbered 0, 4, 8, and 12 is rolled.

(a) Define the mgf of X.

(b) Define the mgf of Y.

(c) Let W = X + Y, the sum when the pair of dice is rolled. Find the mgf of W.

(d) Give the pmf of W; that is, determine P(W = w), w = 0,1, . . . ,15, from the mgf of W.

(a) Define the mgf of X.

(b) Define the mgf of Y.

(c) Let W = X + Y, the sum when the pair of dice is rolled. Find the mgf of W.

(d) Give the pmf of W; that is, determine P(W = w), w = 0,1, . . . ,15, from the mgf of W.

**View Solution:**## Answer to relevant Questions

The number of accidents in a period of one week follows a Poisson distribution with mean 2. The numbers of accidents from week to week are independent. What is the probability of exactly seven accidents in a given three ...Let X1 and X2 be two independent random variables. Let X1 and Y = X1 + X2 be χ2(r1) and χ2(r), respectively, where r1 < r. (a) Find the mgf of X2. (b) What is its distribution? Let n = 9 in the T statistic defined in Equation 5.5-2. (a) Find t0.025 so that P(−t0.025 ≤ T ≤ t0.025) = 0.95. (b) Solve the inequality [−t0.025 ≤ T ≤ t0.025] so that μ is in the middle. Let Y = X1 + X2 + · · · + X15 be the sum of a random sample of size 15 from the distribution whose pdf is f(x) = (3/2)X2, −1 < x < 1. Using the pdf of Y, we find that P(−0.3 ≤ Y ≤ 1.5) = 0.22788. Use the central ...Suppose that among gifted seventh-graders who score very high on a mathematics exam, approximately 20% are left-handed or ambidextrous. Let X equal the number of left-handed or ambidextrous students among a random sample of ...Post your question