Fix A and α > 0 and let h(x ) = Ae-oz for x > 0 and 0 otherwise (a) Compute h(k). (b) Let f(x)-(s...
2. Let X and Y be continuous random variables with joint probability density function fx,y(x,y) 0, otherwise (a) Compute the value of k that will make f(x, y) a legitimate joint probability density function. Use f(x.y) with that value of k as the joint probability density function of X, Y in parts (b),(c).(d),(e (b) Find the probability density functions of X and Y. (c) Find the expected values of X, Y and XY (d) Compute the covariance Cov(X,Y) of X...
Let X and Y have joint density xY)0otherwise. 0 otherwise (a) Find k. (b) Compute the marginal densities of X and of Y (c) Compute P(Y 2x). (d) Compute P(X-Y| 〈 0.5). (e) Are X and Y independent?
0, otherwise Let f(x,y)= 2. a. Sketch the region of integration b. Find k c. Find the marginal density of X d. Find the marginal density of Y e. Find P(Y > 0/X = 0.50) 0, otherwise Let f(x,y)= 2. a. Sketch the region of integration b. Find k c. Find the marginal density of X d. Find the marginal density of Y e. Find P(Y > 0/X = 0.50)
4. Let X have the following PDF: sin(x) , 0 < x < π , otherwise Ix(x) = 0 Find the CDF of X Using the Probability Integral Transformation Theorem, describe the process of generating values from the density of X Using R, generate 1,000 values using your process in part b. Produce a histogram of these generated values, and overlay the density curve of X over top. (Hint: in R, the function acos calculates the inverse cosine function.) Using...
Let f(x) = x.a) Expand f(x) in a Fourier cosine series for 0 ≤ x ≤ π.b) Expand f{x) in a Fourier sine series for 0 ≤ x < π.c) Expand fix) in a Fourier cosine series for 0 ≤ x ≤ 1.d) Expand fix) in a Fourier sine series for 0 ≤ x < 1.
Let α and β be real numbers with 0 < α < βく2m and let h : [α, β] → R>o be a continuous function that is always positive. Define Rh,a to be the region of the (x,y)-plane bounded by the following curves specified in polar coordinates: r-h(0), r-2h(0), θ α, and θ:# β. 3. (a) Show that (b) (c) depends only on β-α, not on the function h. Evaluate the above integral in the case where α = π/4...
Let X be a continuous random variable with PDF f(x) = { 3x^3 0<=x<=1 0 otherwise Find CDF of X FInd pdf of Y
2.4. Compute and plot y[n] - x[n] * h[n], where x[n] - 0, otherwise 1. 4 sn s 15 0, otherwise h[n] = 2.6. Compute and plot the convolution y[n] - x[n] * h[n], where 2.1. Let x[n] = δ[n] + 2δ[n-1]-δ[n-3] and h[n] = 2δ[n + 1] + 2δ[n-l]. Compute and plot each of the following convolutions: (a) y [n] x[n] * h[n] (c) y3 [n] x[n] * h[n + 2]
(1 point) Let f(x Scxºy? if 0 < x < 1, 0 SY51 otherwise Find the following: (a) c such that f(x,y) is a probability density function: c= (b) Expected values of X and Y: E(X) = E(Y) = 100 (c) Are X and Y independent? (enter YES or NO)
2. (24 pts) Let f(x) = >>= {* Ae Mc 1>C where A,B,C ER, A, B +0. x <C' (a) Show that f is differentiable at x = C. (b) Determine the first four terms of the Taylor series centered at x = C for f(x) using the definition of Taylor series. (c) If possible, find the Taylor series T(2) centered at x = C for f(x). (d) What's the radius and interval of convergence? (e) Find R4(C++). Can you...