The random variable V has PMF

(a) Find the value of the constant c.
(b) Find P[V ∈ {u2|u = 1, 2, 3, ... }].
(c) Find the probability that V is even.
(d) Find P[V > 2].
Problem1 Random variable Y has a probability mass function (pmf) as py(y) = a) Find the value of the constant c ,y=1,2,3 , y =-1,-2,-3 0 otherwise b) Now that the constant c is determined, find (G) Probability of Y 1 (ii) Probability of Y<1
Let X be a discrete random variable with PMF: a. Find the value of the constant K b. Find P(1 < X ≤ 3)
Question 4. [5 marksi Let Xbe a random variable with probability mass function (pmf) A-p for -1, 2,... and zero elsewhere (whereq-1-p, 0 <p< (a) Find the moment generating function (mg ofX. C11 (b) Using the result in (a) or otherwise find the expected value and variance of X. C23 (c) Let X, X,., X, be independent random variables all with the pmf fix) above, and let Find the mgf and the cumulant generating function of Y.
5. Let X be a discrete random variable with the following PMF: for x = 0 Px(x)- for 1 for x = 2 0 otherwise a) Find Rx, the range of the random variable X. b) Find P(X21.5). c) Find P(0<X<2). d) Find P(X-0IX<2)
2. The random variable X has PMF Joc, if x = 1,2,3,4 px(x) = 10 otherwise. (a) Calculate the value of c. (b) Calculate the probability that X is an even number. (c) Calculate the probability that X is greater than 2. (d) Calculate the expectations of X and X2. (e) Calculate the variance of X (f) Compare the variances of X, X and vX, without actually calculating the variances. (02, X, X, X . A2)
Let X be a discrete random variable with the following PMF. Px(k) = 1/4 for k = -2 1/8 for k = -1 1/8 for k = 0 1/4 for k = 1 1/4 for k = 2 0 otherwise Define a new random variable Y = (X + 1)2 a) Find E[X] and Var[X] b) Find the range of Y and write its PMF. c) Show that the PMF of Y is a valid PMF. d) Find P(Y ≤...
Suppose a random variable X has a pmf p(x) = [3^(x-1)] / [4^x] , x = 1, 2, ... (a) Find the moment generating function of X. (b) Give a realistic example of an experiment that this random variable can be defined from its sample space. (c) Find the mean and variance of X.
Let X be a discrete random variable with PMF(a) Find P(X ≤ 9). (b) Find E[X] and Var(X). (c) Find MX(t), where t < ln 3.
2. Det X be a geometric random variable with mean S. Define a new random variable Y using the following function Y-11,-31 ifXcS 2 ifX25 Where| | denote the absolute value. (a) Find the PMF ofY (b) Find the CDF of Y (c) Find E[Y] and Var(Y] (d) Find P IYel Y 3]
2. Det X be a geometric random variable with mean S. Define a new random variable Y using the following function Y-11,-31 ifXcS 2 ifX25 Where| |...
Let X be a discrete random variable with a probability mass function (pmf) of the following quadratic form: p(x) = Cx(5 – x), for x = 1,2,3,4 and C > 0. (a) Find the value of the constant C. (b) Find P(X ≤ 2).