The variance of f(x) is defined by: varlf]- E[(f(x) E[f(x)])21 Using this formula derive the following:
The conditional variance of X, given Y, is defined by Prove the conditional variance formula, namely, Var(X) E[Var(X|Y)] Var(E[XYl) Use this to obtain Var(X) in Example 1 S(B) and check your result by differentiating the generating function
5. (10 points) Derive the following formula for f(x) f(4(x+)-3f(x)-f(x+2h)) and show that error is OCh 5. (10 points) Derive the following formula for f(x) f(4(x+)-3f(x)-f(x+2h)) and show that error is OCh
Recall that the variance of a random variable is defined as Var[X]=E[(X−μ)2], where μ = E[X]. Use the properties of expectation to show that we can rewrite the variance of a random variable X as Var [X]=E[X^2]−(E[X])^2 Problem 3. (1 point) Recall that the variance of a random variable is defined as Var X-E(X-μ)21, where μ= E[X]. Use the properties of expectation to show that we can rewrite the variance of a random variable X as u hare i- ElX)L...
3h Q6. Consider f'(X) f2 -f- hf"C) 2 1. Derive the formula using Taylor expansion. 2. Derive the formula using Lagrange interpolation. 3. Find the optimal h.
For the next estimate, derive the formula for the variance of the following estimator, assume that they are three independent samples. (10 pts) Xi is a random variable with mean = μi and variance = σ2i P5A2: If three initial samples are taken. With the following results. A o X2+2X2 3X3 Population Sample size Sample average sample variance 1 40 110.1 6.1 2 50 125 7.2 3 60 85 6.4
1. Suppose the a function g(x) is defined according to the formula f(c) 3(x + 2) +2 for – 3 <x< -2 (x+2)+1 for-2<x< -1 (+2)+1 for - 1<x<1 2 for r=1 for > 1 y 3+ 21 11 1 -2 1 2 (a) Compute f(a) for each of a = -2, -1,0,1,2. (b) Determine lim f(x) and lim f(x) for each of a = -2,-1,0,1,2. (c) Determine lim f(a) for each of a = -2,-1,0,1,2. If the limit fails...
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
Need help with e) and f). e) Derive a formula and give the numerical value for the input power factor of Phase A. f) Derive a formula and give the numerical value for the THD of the line current ia(t) Q3: Three-phase rectifier with six diodes [15pts] The three-phase diode-rectifier below has six diodes and a purely resistive load Rout. The sinusoidal input voltage sources (with a phase difference of 120') are star-connected and have the line-to- neutral amplitude Vn...
Derive the shortcut formula from the definition of the variance of discrete distributions.
The definitional formula for variance is stated in terms of how variance is defined. Question 28 options: True False