Let X be a discrete random variable, and let Y X (a) Assume that the PMF...
Let X be a discrete random variable with the following PMF 6 for k € {-10,-9, -, -1,0, 1, ... , 9, 10} Px(k) = otherwise The random variable Y = g(X) is defined as Y = g(x) = {x if X < 0 if 0 < X <5 otherwise Calculate E[X], E[Y], var(X), and var(Y) for the two variables X and Y
Let X be a discrete random variable with PMF: a. Find the value of the constant K b. Find P(1 < X ≤ 3)
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)
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.
4- Let Y = X, where X is a discrete uniform integer random variable in the range [-4,4). a) What is the PMF of the variable X? b) What is the PMF of the variable Y? c) Draw the PMF of the variables X, and Y. d) Draw the CDF of the variables X, and Y. e) What is the expected value of the random variables X and Y? f) What is the variance of the random variables X and...
3. Let X be a discrete random variable with the following PMF: 0.1 for x 0.2 for 0.2 for x=3 Pg(x)=〈 0.1 for x=4 0.25 for x=5 0.15 for x=6 otherwise a) (10 points) Find E[X] b) (10 points) Find Var(X) c) Let Y-* I. (15 points) Find E[Y] II. (15 points) Find Var(Y) X-HX 4. Consider a discrete random variable X with E [X]-4x and Var(X) = σ. Let Y a. (10 points) Find E[Y] b. (20 points) Find...
Let X be a discrete random variable with the following pmf 0.1 for I = 0.2 0.2 for x = 0.4 0.2 for x = 0.5 P(X = x) = 0.3 for x = 0.8 0.2 for x = 1 0 otherwise Note: Write your final answers as decimals Find the following a) P(0.25 < X < 0.75) = b) P(X = 0.2|X<0.6) c) E(2X+1) =
0.25 x-1 0.15 x2 6. Let X be a discrete random variable with PMF: Px(x) 0.2 x-3 0.1 x 4 0.3 x-5 0 otherwise a. (10 points) Find E[X] b. (5 points) Find Var(X)
Let X be a discrete random variable with pmf p(n) = (n−1)(0.4)2(0.6)n−2, n ≥ 2 and 0 otherwise. Find the mode of X
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