Problem 6: Nonlinear Channel Suppose a transmitter sends a signal X over a channel, where X is exponentially distributed with mean 1. The channel non-linearly distorts the transmitted signal, such th...
Problem 6: Nonlinear Channel Suppose a transmitter sends a signal X over a channel, where X is exponentially distributed with mean 1. The channel non-linearly distorts the transmitted signal, such that the signal at the receiver is given by Y-1-e-Ax, where λ > 0 is a constant. The receiver then estimates X using a linear estimator X based on Y which minimizes the mean squared error between X and X. Find this linear estimator Problem 6: Nonlinear Channel Suppose a...
Problem 5: Noisy Signal A signal generator generates a random sinusoid, X cos (2nt + Θ) whose amplitude is given by a random variable X uniformly distributed between-1 and 1, and phase Θ is an independent random variable which takes each of the following values π 0, π with equal prob- ability. This signal's amplitude is additively corrupted by independent noise YN(0, 0.01) The output amplitude is denoted by Z, where Z-X +Y. Assuming that an estimator of X has...
2. Let X and Y be independent, exponentially distributed random variables where X has mean 1/λ and Y has mean 11. (a) What is the joint p.d.f of X and Y? (b) Set up a double integral for determining Pt < X <Y). (c) Evaluate the above integral. (d) Which of the following equations true, and which are false? (e) Compute PIZ> t where t20. (f) Compute the pd.f. of Z. Z = min(X,Y)
2. Let X and Y be independent, exponentially distributed random variables where X has mean 1/λ and Y has mean 1/μ. (a) What is the joint p.d.f of X and Y? (b) Set up a double integral for determining Pt <X <Y) (c) Evaluate the above integral. (d) Which of the following equations true, and which are false? {Z > t} = {X > t, Y > t} (e) Compute P[Z> t) wheret 0. (f) Compute the p.d.f. of Z.
1. Which of the following conditions will lead to a smaller variance for the intercept estimator for your multiple regression model? (A) X values cluster far from the origin of the X axis (B) X values closely pack around the mean of X in your sample (C) Small sample sizes (D) High correlation among the explanatory variables (E) Small error variance in the population regression function 2. R-squared (A) measures the proportion of variability of the dependent variable that is...