Consider a Gaussian random variable X with mean 8 and variance 3. Find z if P[X>10]=1- (phi)(Z)
Consider a Gaussian random variable X with mean 8 and variance 3. Find z if P[X>10]=1-...
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 =...
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].
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
Consider the normal random variable X with mean 3 and variance 4. Find the best Chernoff estimate on P(X>=5). Please do not use Z-table or Z-test. Solve only using Chernoff estimate. Thanks.
8. A Gaussian random variable x with a mean and variance of ax and Ox? respectively goes through a linear transformation of y=ax +b, where a and b are any real constants. Determine the probability density function of y, also give its mean and variance. (5 points).
Suppose X is a Gaussian random variable with mean 2 and variance 4. Find E(eX/2).
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)
8. A random variable X has a mean u = 10 and a variance o= 4. Using Chebyshev's theorem, find (a) P(X – 10 > 3); (b) P(X - 10 < 3); (c) P(5< X < 15); (d) the value of the constant c such that P(X – 10 > c) <0.04.
Stochastic Signal Theory 1. The random variable A is Gaussian distributed with mean 10 and standard deviation e20 A random process X (t) is a function of A defined by the given equation. Use this information to answer the questions below. (24 points) X(t)- Ae'cos(t) (a) Find the mean function for X(t). (b) Find the variance function for X(t). (c) Find the autocovariance function for X (t). Stochastic Signal Theory 1. The random variable A is Gaussian distributed with mean...