For a discrete random variable Y, you are given: Py(z)= · Calculate ELY2]
For a discrete random variable X, you are given: E (0.3t 0.7)8 Calculate the coefficient of t3 in the probability generating function, Px(t) A0.058 B 0.254 С 0.296 D 0.508 E 0.806
Suppose three random variables X, Y, Z have a joint distribution PX,Y,Z(x,y,z)=PX(x)PZ∣X(z∣x)PY∣Z(y∣z). Then X and Y are independent given Z? True or False Suppose random variables X and Y are independent given Z , then the joint distribution must be of the form PX,Y,Z(x,y,z)=h(x,z)g(y,z), where h,g are some functions? True or false
Name: Question 4. Let Y be a discrete random variable with ply) given in the table below. p(y0.2 0.30.5 a) Find the cumulative distribution function (CDF)Fy) Be sue to specify the value of Fly) for all y,y b] Sketch the distribution function given in part [a]
Q6 (4pt) Let X be a discrete uniform random variable over {1,2,...,6} and let Y be a Bernoulli random variable with parameter 1/2 such that X, Y are independent. (1) Find the PMF of the random variable Z, where Z XY. (2) Compute the third moment of Z, that is, E[z2
If the joint probability distribution of three discrete random variables X, Y , and Z is given by: f(x, y, z) = (x + y)z / 63 , for x = 1, 2; y = 1, 2, 3; z = 1, 2. Find the probability P(X = 2, Y + Z ≤ 3)
Problem 3 A discrete random variable Y takes values {k= 0, 1, 2, ...,} such that PLY Z k} = ()* for k 20. 1. Derive P[Y = k) for any k > 0. 2. Evaluate expectation, E[Y] = 3. Given E[Y(Y - 1)] = 15 , find variance of Y, Var[Y] =
Exercise 2. The transform associated uwrith a random variable Y has the form Y(s)a Find a, py(41), py(11), the third largest possible value of Y, and its corresponding probability. Justify your answer.
Exercise 2. The transform associated uwrith a random variable Y has the form Y(s)a Find a, py(41), py(11), the third largest possible value of Y, and its corresponding probability. Justify your answer.
Random variables X and Y are independent. the random variable X has density p(x) and Y is a discrete random variable having just two values: 1 with probability 1/3 and 2 with probability 2/3. Calculate the density of Z=X+Y.
Let X be a discrete random variable, and let Y X (a) Assume that the PMF of X is Ka2 0 if x- -3, -2,-1,0,1,2,3 otherwise, where K is a suitable constant. Determine the value of K. (b) For the PMF of X given in part (a) calculate the PMF of Y (c) Give a general formula for the PMF of Y in terms of the PMF of X
Z table.pdf Question 6 4 pts X is a discrete random variable that represents the number of student emails that a professor receives in any given day. The probability distribution for X is summarized in the table below: PIX = x) Calculate the mean of X. Provide a numeric value rounded to two decimal places. Previous Next