for a random variable (X), V(8x-14) =
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4 X is a random variable with E(X) = 100 and V(X) = 15. Find (a) E(X2). (b) E(3X + 10). (c) E(-X). (d) V(-X). (e) D(-X).
X is a discrete random variable with E(X) = 1 and V(X)=1/4=0.25. Y is a discrete random variable with E(Y) = -1 and V(Y)=1/25=0.04. If X and Y are independent variables, what is the value of δ(X+Y)?
X is exponential random variable with λ = 3. A) Calculate E(X"2) of this random variable. B) Calculate V(X 2)
4. [-14 Points] DETAILS (4pt) The variance of random variable X is 1 and the variance of random variable Y is 4. The correlation coefficient between the two random variables X and Y is 0.2. (a) (1pt) Find the covariance between X and Y. (b) A new random variable Z is given by Z = 2X + 1. Find the covariance between X and Z. (1pt) Find the covariance between Y and Z. (2pt)
The velocity of a particle in a gas is a random variable X with probability distribution fX (x) = 256 x^2 e^(−8x) x > 0. The kinetic energy of the particle is Y = (1/2 )* (mX^ 2). Suppose that the mass of the particle is 49 yg. Find the probability distribution of Y. (Do not convert any units.)
Suppose V is a zero-mean Gaussian random variable, and define the random processes X(t) = Vt and Y(t) = V2t for −∞ < t < ∞. a)Find the crosscorrelation function for these two random processes. b)Are these random processes jointly wide-sense stationary?
Suppose V is a zero-mean Gaussian random variable, and define the random processes X(t) = Vt and Y(t) = V2t for −∞ < t < ∞. a)Find the crosscorrelation function for these two random processes. b)Are these random processes jointly wide-sense stationary?
Problem 9: Suppose X is a continuous random variable, uniformly distributed between 2 and 14. a. Find P(X <5) b. Find P(3<X<10) c. Find P(X 2 9)
(5 pts) Consider a random variable X with pdf V o S 0.5eX fx(x) = { 0.5e-2 x < 0 x > 0. 0.5 e-> o ΔΙ Let S 4x2 x < 0 g(x) = { 22 x 20, V ΔΙ and let Y = g(X). Determine fy(y).
Suppose that a random variable X satisfies E (3X − 6) = 3 and V ar [2X + 1] = 16. Use Chebyshev’s Inequality to bound P (X ≥ 17).