X1 and X2 are discrete random variables (and are independent) with probability functions:
p1(x1) = 1/3 for x1 = −2 ,−1 , 0
p2(x2) = 1/2 for x2 = 1, 6
Let Y = X1 + X2
a).
Find the MGF of X1, X2 and Y
b).
USE MGFS derived in part a) to determine the probability mass function of Y.
Note: MGFs in part a) must be used to determine the pmf of Y in part b)
X1 and X2 are discrete random variables (and are independent) with probability functions: p1(x1) = 1/3...
W1 and W2 are discrete random variables (and are independent) with probability functions: p1(w1) = 1/6 for w1 = −2 ,−1 , 0 p2(w2) = 1/4 for w2 = 1, 6 Let Y = W1 + W2 a). Find the MGF of W1, W2 and Y b). USE RESULTS IN PREVIOUS PART to determine the probability mass function of Y
W1 and W2 are discrete random variables (and are independent) with probability functions: p1(w1) = 1/6 for w1 = −2 ,−1 , 0 p2(w2) = 1/4 for w2 = 1, 6 Let Y = W1 + W2 Find the distribution and probability mass function of Y (Hint: First find MGF of W1 and W2 and then find MGF of Y)
Let X1 and X2 be two discrete random variables, where X1 can attain values 1, 2, and 3, and X2 can attain values 2, 3 and 4. The joint probability mass function of these two random variables are given in the table below: X2 X1 2 3 4 1 0.05 0.04 0.06 2 0.1 0.15 0.2 3 0.2 0.1 0.1 a. Find the marginal probability mass functions fX1 (s) and fX2 (t). b. What is the expected values of X1...
Let X1 and X2 be random variables, not necessarily independent. Show that E [X1 + X2] = E [X1] + E [X2]. You may assume that X1 and X2 are discrete with a joint probability mass function for this problem, while the above inequality is true also for continuous random variables.
Let Y1 and Y2 be two independent discrete random variables such that: p1(y1) = 1/3; y1 = -2 ,- 1, 0 p2(y2) = 1/2; y2 = 1, 6 Let K = Y1 + Y2 a) FInd the moment Generating function of Y1, Y2, and K b) find the probability mass function of K
PLEASE MAKE YOUR HAND WRITING CLEAR AND READABLE . THANK YOU! O Let X and Y be independent random variables with a discrete uniform distribution, i.e., with probability mass functions for k = 1, px(k) = py (k) =-, N. Use the addition rule for discrete random variables on page 152 to determine the probability mass function of Z -X+Y for the following two cases. a. Suppose N = 6, so that X and Y represent two throws with a...
13. Let X1, X2, ...,Xy be a sequence of independent and identically distributed discrete random variables, each with probability mass function P(X = k)=,, for k = 0,1,2,3,.... emak (a) Find the expected value and the variance of the sample mean as = N&i=1X,. (b) Find the probability mass function of X. (c) Find an approximate pdf of X when N is very large (N −0).
Let Xi and X2 independent random variables, with distribution functions F1, and F2, respectively Let Y a Bernoulli random variable with parameter p. Suppose that Y, X1 and X2 are independent. Proof using the de finition of distribution function that the the distribution function of Z =Y Xit(1-Y)X2 is F = pF14(1-p)F2 Don't use generatinq moment functions, characteristic functions) Xi and X2 independent random variables, with distribution functions F1, and F2, respectively Let Y a Bernoulli random variable with parameter...
2. Let X and Y be two independent discrete random variables with the probability mass functions PX- = i) = (e-1)e-i and P(Y = j-11' for i,j = 1, 2, Let {Uni2 1} of i.i.d. uniform random variables on [0, 1]. Assume the sequence {U i independent of X and Y. Define M-max(UhUn Ud. Find the distribution
6. The Poisson distribution is commonly used to model discrete data. The probability mass function of a Poisson random variable is P(X = x/A) =ー厂 , x = 0, 1, 2, , λ > 0. a. Find the MGF of a Poisson random variable. b. Use the MGF to find the mean of a Poisson random variable c. Use the MGF to find the second raw moment of a Poisson random variable. d. Use results d. Let Xi and X2...