Suppose X is a Gaussian random variable with mean 2 and variance 4. Find E(eX/2).
Suppose X is a Gaussian random variable with mean 2 and variance 4. Find E(eX/2).
Consider a Gaussian random variable, X, with mean /i and variance o7. Find E[X |X >fu+a] Consider a Gaussian random variable, X, with mean /i and variance o7. Find E[X |X >fu+a]
A Gaussian random variable X has mean 2 and variance 4 a) Find P(X < 3). (b) Find P(1 < X < 3) (c) Find P({X > 4}|{X > 3}) (d) Let Y = X^2 . Find E[Y].
1. The random variable X is Gaussian with mean 3 and variance 4; that is X ~ N(3,4). $x() = veze sve [5] (a) Find P(-1 < X < 5), the probability that X is between -1 and 5 (inclusive). Write your answer in terms of the 0 () function. [5] (b) Find P(X2 – 3 < 6). Write your answer in terms of the 0 () function. [5] (c) We know from class that the random variable Y =...
Suppose that X is a Gaussian Random Variable with zero mean and unit variance. Let Y=aX3 + b, a > 0 Determine and plot the PDF of Y
X is a Gaussian random variable with zero mean and variance ơ2 This random variable 5 20 points is passed through a quantizer device whose input-output relation is g(z) = Zn, for an x < an+1, 1 N where In lies in the interval [an, Qn+1) and the sequence fa, a2, al z-00, aN41 # oo, and for i > j we have ai > aj. Find the PMF of the output random variable Y g(X). aN+1) satisfies the conditions
blem 4 , The input to a system is a Gaussian random variable below X with zero mean and variance of σ as shown System The output of the system is a random variable Y given as follows: bX (a) Determine the probability density function of the output Y b) Now assume that the following random variable is an input to the system at time t: where the amplitude A is a constant and phase θ is uniformly distributed over...
Consider a Gaussian random variable X with mean 8 and variance 3. Find z if P[X>10]=1- (phi)(Z)
Let ˜x and ˜y be zero-mean, unit variance Gaussian random variables with correlation coefficients, . Suppose we form two new random variables using linear transformations: Let and be zero-mean, unit variance Gaussian random variables with correlation coefficients, p. Suppose we form two new random variables using linear transformations: Find constraints on the constants a, b, e, and d such that ù and o are inde- pendent.
5. [20 points] X is a Gaussian random variable with zero mean and variance σ2. This random variable is passed through a hard-limiter device whose input-output relation is b r <0 Find the PDF of the output random variable Yg(X)
The input to a system is a Gaussian random variable below X with zero mean and variance of σ- as shown x System The output of the system is a random variable Y given as follows: -a b, X>a (a) Determine the probability density function of the output Y (b) Now assume that the following random variable is an input to the system at time t: where the amplitude A is a constant and phase s uniformly distributed over (0,2T)....