Please answer Problem 18 Problem 17 Find the constant k that makes the following functions PDFs....
7. Given the joint density function /(x,y) =(kx (1 + 3 y*) 0<x<2,0<p?1 elsewhere a. Find k, g() h) and f(x) b. Evaluate P(-<X<1)
What is the constant k that makes the following function a valid pdf? fX(x) = kx2(1-x)7 for 0 ≤ x ≤ 1, fX(x) = 0 otherwise
2. Let the random variables X and Y have the joint PDF given below: (a) Find P(X + Y ≤ 2). (b) Find the marginal PDFs of X and Y. (c) Find the conditional PDF of Y |X = x. (d) Find P(Y < 3|X = 1). Let the random variables X and Y have the joint PDF given below: 2e -0 < y < 00 xY(,) otherwise 0 (a) Find P(XY < 2) (b) Find the marginal PDFs of...
Please solve the normalization, 7e, and the commutator questions 6. Normalization Normalize the following functions: sin (1") between 0<x<L 200 for 0 <r <o, treating do as a constant 7. Eigenfunctions and Eigenvalues Determine which of the following are eigenfucntions of the operator 4 give the eigenfunction. Where appropriate (a) pikx (b) cos ka (c) k (d) kx (e) e-ax? 8. Commutator Evaluate the commutator (î, P2]
Q2) (20 points) The joint pdf of a two continuous random variables is given as follows: < x < 2,0 < y<1 (cxy0 fxy(x, y) = } ( 0 otherwise 1) Find c. 2) Find the marginal PDFs of X and Y. Make sure to write the ranges. Are these random variables independent? 3) Find P(0 < X < 110 <Y < 1) 4) What is fxy(x\y). Make sure to write the range of X.
For each of the following functions, (i) find the constant c so that f(x) is a pdf of a random variable x, (ii) find the cdf F(x)-P(XSX), (iii) sketch graphs of the pdf f (x) and the distribution function F(x), and (iv) find μ and σ2. (a) f (x) x3/4, 0 <x<c (b) f (x)-(3/16x-,-c < x c
The circled answer is wrong, please show steps to arrive at a correct answer. (17) Assume X and Y have the following joint density function: f(x,y) =-(x + y), 0<x<2,0<p<2 Calculate P(X +Ys 1). B) C) 17 24 A) E) 24 24
Problem 17 Find the directional derivative at the point (-1,1) Problem 18 In what direction is the function (x,y) - cos(^) sin(y sloping most steeply doumhall at the point (r/A,x/0) Recall that a directiom is rported as a unsit wector. Problem 17 Find the directional derivative at the point (-1,1) Problem 18 In what direction is the function (x,y) - cos(^) sin(y sloping most steeply doumhall at the point (r/A,x/0) Recall that a directiom is rported as a unsit wector.
3.3. Are the following valid PMFs? If yes, find the constant k that makes it so. a) p(z) (1-2)/k for z = 1,2, , 5 b) p(x)2)/k for 1,2,..,5 뎅 “..
Find the Fourier series of the following functions in the given intervals. f(x) = r +, - <x< g(t) = { inter) 0. -T<r <0, sin(x), 0<x< 1.