Let X be a discrete random variable that is equally likely to be integers in the range [a,b], where a and b are integers with a<0<b. Find the PMF of the random variable Y = max(0,X).
Let X be a discrete random variable that is equally likely to be integers in the range [a,b], where a and b are integers...
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...
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
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.
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
Let X be a discrete random variable with PMF: a. Find the value of the constant K b. Find P(1 < X ≤ 3)
Let X be a discrete random variable with Pr{X = i} = ci for positive, odd integers 3 ≤ i ≤ 13; otherwise, the probability is zero. (a) Compute E[min(9,X)]. (b) Compute E[(X − 9)+] where x+ = max(x, 0).
4. Let X be a discrete random variable with PrX-ici for positive, odd integers 3 Sis 13; otherwise, the probability is zero a) Compute the value of c. (b) What is the mean of X? (c) What is the second moment of X (that is, E[X21)? (d) What is the variance of X? (e) Compute E[min(9, X) (f) Compute E(X-9)*) where x+ = max(x,0).
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 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).