2. Let X and Y be two independent discrete random variables with the probability mass functions...
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...
Let X and Y be independent random variables. Random variable X has a discrete uniform distribution over the set {1, 3} and Y has a discrete uniform distribution over the set {1, 2, 3}. Let V = X + Y and W = X − Y . (a) Find the PMFs for V and W. (b) Find mV and (c) Find E[V |W >0].
Problem 5 Define X and Y to be two discrete random variables whose joint probability mass function is given as follows: e-127m5n-m P(X = m, Y = n) = m!(n - m)! for m <n, m> 0 and n > 0, while P(X = m, Y = n) = 0 for other values of m, n 1. Calculate the probability that 1 < X <3 and 0 <Y < 2. 2. Calculate the marginal probability mass functions for the random...
Let X and Y denote independent random variables with respective probability density functions, f(x) = 2x, 0<x<1 (zero otherwise), and g(y) = 3y2, 0<y<1 (zero otherwise). Let U = min(X,Y), and V = max(X,Y). Find the joint pdf of U and V.
pleaze help me fast 2. Let X and Y be discrete random variables with joint probability mass function X=1 X=5 Y=1 5a За Y=5 4a 8а a. What is the value of a? b. What is the joint probability distribution function (PDF) of X and Y? c. What is the marginal probability mass function of X? d. What is the expectation of X? e. What is the conditional probability mass function of X given Y = 1? f. Are X...
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)
Proposition 6.10 Independent Discrete Random Variables: Bivariate Case Let X andY be two discrete random variables defined on the same sample space. Then X and Y are independent if and only if pxy(x,y) = px(x)py(y), for all x , y ER. (6.19) In words, two discrete random variables are independent if and only if their joint equals the product of their marginal PMFs. Proposition 6.11 Independence and Conditional Distributions Discrete random variables X and Y are independent if and only...
Let X and Y be continuous and independent random variables, both with uniform distribution (0,1). Find the functions of probability densities of (a) X + Y (b) X-Y (c) | X-Y |
Let X and Y be two discrete random independent random variables. p(x) = 1/3 for x =-2,-1,0 p(y) = 1/2 for y =1,6 Z = X + Y. What is the distribution of Z using the method of MGF's
The next two problems allow you to express the sum of two independent random as a precise function of each of their probability mass functions or probability density functions in the case they are each discrete or continuous random variables respectively. These problems are conceptually important because they tell you how to compute the distribution of a random walk (which we will define later) from the distribution of its steps (again, defined later) in a general case. 5. Let X,...