Find the fourier series و = (x) 1, 18, - 7<<0 0 << ;}
(b) Let X have the pdf x? f(x)= ;-3<x<3, 18 = zero elsewhere. (i) Find the cdf of X
Let X be a random variable with pdf S 4x3 0 < x <1 Let Y 0 otherwise f(x) = {41 = = (x + 1)2 (a) Find the CDF of X (b) Find the pdf of Y.
3. (15 pts) Let D be an infinite set with cardinal d. Let A = {X C D | 0(X) <3}. Prove that o(A) = d.
let X be s random nareprion if x <0 > 0 (a) Let M= {X > 1). Find Fx( M)
Find the product. Leave the result in trigonometric form. (Let 0° s O < 360°.) (cos 2° + i sin 2°) (cos 24° + i sin 24°) x
5) In Goy), with inner product < 1.8>]s«g(x)dx, let S(x)=x"$(x)=x', a) Computer />; b) Find the "angle" between the two functions.
QUESTION 18 Let M and m denote the maximum and the minimum values of f(x, y) = x2 - 2x + y2 +3 in the disk 2? + y2 < 1. Find M + m. OA 8 OB. 7 Ос 5 OD 4 OE 12
3. Let X be a continuous random variable with probability density function ax2 + bx f(0) = -{ { for 0 < x <1 otherwise 0 where a and b are constants. If E(X) = 0.75, find a, b, and Var(X). 4. Show that an exponential random variable is memoryless. That is, if X is exponential with parameter > 0, then P(X > s+t | X > s) = P(X > t) for s,t> 0 Hint: see example 5.1 in...
Need help please the steps, thanks. K=2 (i) Let 0 < x < 1; et f(x) x tk, 1<x<2, } the Fourier series at x = 1. مر and let f(x) be 2-periodic. Find the value of