We have given x1 and x2 are numerical values in the range of X
Option D) is correct.
F(x1)
Suppose that X is a discrete random variable with pmf, p(x), arn x1 and x2 be...
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)
Problem 3. Let X be a discrete random variable, with probability distribution P(X X1) = 0.95, P(X X2) = 0.05. Determine x, and X2 such that E(X-0 and σ2(X) = 7.
Let X1 and X2 be two discrete random variables, where X1 can attain values 1, 2, and 3, and X2 can attain values 2, 3 and 4. The joint probability mass function of these two random variables are given in the table below: X2 X1 2 3 4 1 0.05 0.04 0.06 2 0.1 0.15 0.2 3 0.2 0.1 0.1 a. Find the marginal probability mass functions fX1 (s) and fX2 (t). b. What is the expected values of X1...
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 PMF(a) Find P(X ≤ 9). (b) Find E[X] and Var(X). (c) Find MX(t), where t < ln 3.
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)
Problem 3. Let X be a discrete random variable, with probability distribution Determine x1 and X2 such that E(X-0 and ơ2(X-7.
2. For a discrete random variable X, with CDF F(X), it is possible to show that P(a < X S b)-F(b) - F(a), for a 3 b. This is a useful fact for finding the probabil- ity that a random variable falls within a certain range. In particular, let X be a random variable with pmf p( 2 tor c-1,2 a. Find the CDF of X b. Find P(X X 5). c. Find P(X> 4). 3. Let X be a...
8. (8 points) Let X1, X2, . . . , X, bea random sample from the geometric distribution with pmf f(aip) (1-P)-p,z1,2,3,..., where 0 <ps 1. Find the maximam likel ihood estimator of p and show that the maximum likelthood estimator is unblased. 8. (8 points) Let X1, X2, . . . , X, bea random sample from the geometric distribution with pmf f(aip) (1-P)-p,z1,2,3,..., where 0
Consider random variables X and Y with the joint pdf fx1,x2(x1,x2) = 3x1, 0 < x2 < x1 <1. Calculate P(X2 < 1/2 | X1 >= 3/4)