If {Y(t)} is the square law detector process and if Z(1) = Y(t) – E{Y(1)}, show that the spectral density of {Z(1)} is given by S„(@) : ÷ Sa@) S„(0 – a) da, %3D xX, where S(@) is the input spectral density.

Q: 2 y

A: According our guidelines i solve only first question.For second solution please resubmit again…

Q: 1. Suppose that X1, X2, · · · , Xn are iid (independent and identically distributed). Let E[Xi ] =…

A: Given that X_n are iid with and ,we can determine the expected value and variance of the sum

Q: 10) y = xtanx + sin-ly

A: according to guidelines we should able to do only one question at a time #10

Q: Let f(x,y, z) = xtan (Vyz)- sin(e*) , evaluate zy %3D дудхда

A:

Q: For the following table, assume that y = a (x ^b). Then 2 7 9 11 11 17 13 25 y = 3.083 x^2.312 O…

A:

Q: Let A = Av = ( 4(Av) = ( -3 4 3 21.₁ ‚ v = (x, y).

A:

Q: Let n I be a positive integer. Show that the functional •1 S[y] = √² dx (y')"e", y(0) = 1, y(1) = A…

A: Given that, n>1 be a positive integer.

Q: Let f(2) = In[="(= + 7)*(z² + 7)°] f'(x) =

A: Given : fx = lnx8x+72x2+76

Q: f(x, y) = 'r cos(y) + y(e² − 1), x‡0 xy 0 x = 0.

A:

Q: Exercise 2. Let x =1 and Ar = 0.001. Find Ay (2a) f(z) = 52? –1 (2b) f(z) =

A: Given data: x=1∆x=0.001 #2a The function is, fx=5x2-1

Q: Compute the inner product = f(x)g(x)dx where f(x) = sin(x) and g(x) = sin(2x)

A:

Q: 19 Let u(x) = sin(x) and v(x) = x¹9 and f(x) = u'(x) = v'(x) = u'v - uv' f' 2² u(x) v(x)

A: sin(x)' = cos(x) dxndx=n.xn-1

Q: Consider the DE y"+exy'+ (sinx) y = ex+2lny then the order of the DE is ✓ and it is

A:

Q: If f (x, y) = Vr³ + y³ In(x² + y²)e*in (zy+y') + x³y+ 10 , then f. (1,0) =

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: Let u: R" x R →→ R caloric. Show the following e" caloric ⇒u constant.

A: Given: u:ℝn×ℝ→ℝ is caloric.   To Show: eu is caloric ⇔ u is constant

Q: Find S'(-1) if #(f(x))'+ 9z°f(x) = 2 and f(-1) = 2 I'(-1) =

A: To find f'(-1) first we differentiate both sides of  the given equation with respect to x and then…

Q: Let F(x) = f(x°) and G(x) = (f(x))* . You also know that a° = 14, f(a) = 2, f'(a) = 3, f'(a") = 6…

A:

Q: (iii) y= x'e**, y = sin x+eec* (iv) sec x

A:

Q: Let F(a) = f(x*) and G(x) = (f(x))". You also know that a = 2, f(a) = 3, f'(a) = 15, f'(a*) = 2 |3D…

A:

Q: m(t) = E[e* ]= £e* p(y) +e +e" for y=1,2,3 | - Is this a valid MGF? Valid-TRUE Non Valid -FALSE

A: Given: The mgf of Y is  mt=EetY=∑y etYpy=et2 121+e2t2 122+e3t2 123    for y = 1, 2, 3

Q: V ss Vst Vts Vtt || || 11 11 V sin(2s² - 4t²)

A:

Q: Find dy/dx for the following : 9) y* = sin-1 x %3D 10) y = xtanx + sin-ly 11) (Vy)* = (In…

A:

Q: X, Y, Z ~ beta (alpha=1, beta=2) => p(X < sqrt(YZ)) = ?

A: In this problem, we are given three random variables X, Y, and Z, which are independently…

Q: Let µ* (E) =0 , then µ * (E U F) =µ* (F) ▼ F C R.

A:

Q: (1) If f(x) = x°, then f'(x) Preview (2) If g(x) = - 2x4, then g'(x) Preview 1 then h'(x) x4 (3) If…

A: 1) If fx=x9 then,  f'x=9x8   2) if gx=-2x4 then, g'x=-8x3

Q: If z = x2 + y?, x = e' cos(s) and y = e' sin(s), then %3D dz at (t, s) = (1,0) is as %3D

A: Given that z=x2+y2, x=etcoss and y=etsins First we have to find ∂z∂s.

Q: If Y Poisson(A) and A has pdf f(A) = e-^ for A > 0, elsewhere, find zero E(2Υ) V (2Y):

A:

Q: Compute the correlation coefficient p for X and Y.

A: The expected value of x2 is,…

Q: Which of f (x) = x sin2 x and g(x) = x2 sin2 x has a larger average value over [0, 1]? Over [1, 2]?

A:

Q: Calculate the first quartile and third qiartile for the data below. Class 5 -7 8 - 10 11 - 13 14 -…

A: The first quartile and third quartile are given by Q1 and Q3 respectively.

Q: 2) z = e* yz-3x yn z, = ? ( x=x(y,z) ) l(0.1,1)

A: