Suppose that X is exponentially distributed with mean 1/2. Which of the following is a density...
Suppose that X is exponentially distributed with mean 1/2. Which of the following is a density function of Y = X? S4ye -2y2 0 y > 0 y < 0 2e-2y y > 0 y < 0 o {:2 2e-2y y > 0 y<0 Site 10 y > 0 y<0 ke-u/2 y y > 0 y < 0 { e-2y2 y > 0 y < 0 0
Suppose that X is exponentially distributed with mean 1/2. Which of the following is a density function of Y = X? S4ye -2y2 0 y > 0 y < 0 2e-2y y > 0 y < 0 o {:2 2e-2y y > 0 y<0 Site 10 y > 0 y<0 ke-u/2 y y > 0 y < 0 { e-2y2 y > 0 y < 0 0
Suppose that X is exponentially distributed with parameter 1 = 4. Given that X=X, Y is normally distributed with mean and standard deviation x. Which of the following is the conditional probability density of Y given X=x? (1/a)2 e 2 72 73 e 2 √2 ay (y/-)2 4e 43 e 2 72 73 4 e 40 e 2 V2 πμ
Suppose that X is exponentially distributed with parameter 1 = 4. Given that X=X, Y is normally distributed with mean and standard deviation x. Which of the following is the conditional probability density of Y given X=x? (1/a)2 e 2 72 73 e 2 √2 ay (y/-)2 4e 43 e 2 72 73 4 e 40 e 2 V2 πμ
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.
3. Suppose that X and Y are independent exponentially distributed random variables with parameter λ, and further suppose that U is a uniformly distributed random variable between 0 and 1 that is independent from X and Y. Calculate Pr(X<U< Y) and estimate numerically (based on a visual plot, for example) the value of λ that maximizes this probability.
Consider an exponentially distributed random variable X with pdf f(x) = 2e−2x for x ≥ 0. Let Y = √X. a. Find the cdf for Y. b. Find the pdf for Y. c. Find E[Y]. If you want to skip a difficult integration by parts, make a substitution and look for a Gamma pdf. d. This Y is actually a commonly used continuous distribution. Can you name it and identify its parameters? e. Suppose that X is exponentially distributed with...
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 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...
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)