7. For the probability density function f(x) = for 0 <<<2 (a) Find P(x < 1) (b) Find the expected value. (c) Find the variance.
Fourier Series please answer no. (2) when p=2L=1 - cos nx dx = bn(TE) +277 f(x) sin nx dx (- /<x< 1 2) p=1 2. f(x) = = COS TEX 3. Find the Fourier series of the function below: f(x) k 2 1-k Simplification of Even and Odd Function:
2. A random variable X has a cdf given by F(x) = 1 . x < 0 0 < x < 1 <3 x > 3 11, (f) What is P(X = 1)? (g) Find E(X), the expectation of X. (h) Find the 75th percentile of the distribution. Namely, find the value of 70.75 SO that P(X < 70.75) = F(710.75) = 0.75. (i) Find the conditional probability P(X > X|X > 3).
11) Find the value of k so that f (x) = kx4(1 -x)2 for 0 <x < 1 is a beta density function Also determine find E(T) and Var (T)
Question. Consider () - ( cos(t), sin(t)) for 0 +< 2. Parameterine this curve by are length. Chat
2. Determine and sketch the spectrum, the Fourier transform, of x() where -2l +cos(0)+ jsin for -<t<
1. If f(x) is a Density Function, what is the value of k? Skr3, 0<x<1, f(0) 0, elsewhere.
Find the exact value of sinſ and cos given that cos x = 3,27 ,270° <x< 360°. [8] 4-cos e 18. cos20-5 cos 0+4 since 1+cos e
f(x)=\x(-2<x<2), p = 4 for the given periodic function, what the Fourier series of f? a. an= 8 -cos(nm) 22 n' bn=0 Ob. 4 an = -COS(nn) n?? 4 bn= n2012 C. an 4 cos(nn) n272 bn=0 O d. an 4 22 [(-1)" – 1] bn=0 e. an= 4. -sin(n) n' 2 bn=0
A periodic function f(x) with period 21 is defined by: X + -1<x< 0 2 f(x) = 0<x< 2 Determine the Fourier expansion of the periodic function f(x). X - TT