2. LetX be a continuous RV uniformly distributed over [O . Let Y-sin(X). Find the pdf...
Let Θ be a continuous random variable uniformly distributed on [0,2 Let X = cose and Y sin e. Show that, for this X and Y, X and Y are uncorrelated but not independent. (Hint: As part of the solution, you will need to find E[X], E[Y] and E|XY]. This should be pretty easy; if you find yourself trying to find fx(x) or fy (v), you are doing this the (very) hard way.) Let Θ be a continuous random variable...
Let X1 , X, , and X3 be independent and uniformly distributed between-2 and 2. (a) Find the CDF and PDF ofYX, +2X2 (b) Find the CDF of Z-), + X, . (c) Find the joint PDF of Y and Z.(: Try the trick in Problem 2(b) Let X1 , X, , and X3 be independent and uniformly distributed between-2 and 2. (a) Find the CDF and PDF ofYX, +2X2 (b) Find the CDF of Z-), + X, . (c)...
Q1. Let X be a random variable uniformly distributed over [-2, 4] (1) Find the mean and variance of X. (2) Let Y 2X+3. Draw the PDF of Y [8 marks] 6 marks] [8 marks (3) Find the mean and variance of Y
Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI <x3) Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI
1. [30pt] Suppose x is uniformly distributed over (-2, 1] and yx 1. Find the pdf , 2. [30pt] Let xi be 1.1 d 1 rend.
Problem 3: Problem 3: (20 points) Suppose X is a uniformly distributed continuous random variable over [1,3]. a. (10 points) If Y - 4X2, find f (y), the PDF of Y. Indicate the range for which it applies. b. (10 points) What is the expected value of Y 0 し( 4 4 Problem 3: (20 points) Suppose X is a uniformly distributed continuous random variable over [1,3]. a. (10 points) If Y - 4X2, find f (y), the PDF of...
Let Θ be a continuous random variable uniformly distributed on [0,2 Let X = cose and Y sin e. Show that, for this X and Y, X and Y are uncorrelated but not independent. (Hint: As part of the solution, you will need to find E[X], E[Y] and E|XY]. This should be pretty easy; if you find yourself trying to find fx(x) or fy (v), you are doing this the (very) hard way.)
(a) Let X(t) sin t, where is uniformly distributed over the interval [0, 27]. Verify (i) The discrete-time process (t), t = 1,2,... is weakly, but not strongly stationary (ii) The continuous-time stochastic process X(t), t> 0 is neither weakly nor strongly stationary (a) Let X(t) sin t, where is uniformly distributed over the interval [0, 27]. Verify (i) The discrete-time process (t), t = 1,2,... is weakly, but not strongly stationary (ii) The continuous-time stochastic process X(t), t> 0...
If X is uniformly distributed over (0,2) and Y is exponentially distributed with parameter λ = 2. Also X and Y are independent, find the PDF of Z = X+Y.
3.39 PDF of the magnitude of a RV. Find the PDF fy (v) of the RV YX in terms of the PDF of the RV X. Write down the explicit expression for fr () if X~N (0,2). In this case, Y is a Rayleigh distributed RV