Exercise 3.68. Let Z~ N(0, 1) and X N(u,o2). (a) Calculate E[Z*). (b) Calculate E[X*].

Q: Given h(x) = (-x² – 2x – 2), find h' (0)-

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Q: If If y + x³y3 =y e\ + 1, y is function of x, then dx 3 x²y³ - y e* 5y* – 3 x³y? – e* 3,2 O 3 x²y³ –…

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Q: 4. Show that if f and g are pdfs and a € [0, 1], then af + (1-a)g is also a pdf.

A: Given that  Show that if ƒ and g are pdfs and α [0, 1]  then αf + (1 -α )g is also a pdf.

Q: If f(x) is a pdf, then f(x) can take any value in R (i.e., f(x) can be any real number). O True…

A: We have given that the statement about to the probability density function (pdf) f(x).

Q: For the function f(x)= 4 e , find f"(x). Then find f"(0) and fP"2).

A: Take derivative with respect to x.

Q: Show that if ƒ (z) = C where C is a constant, then f (s) = C/s for 8 > 0.

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Q: x/c x= 1,2,n Suppose that f(x) = • otherwise Find c so that f(x) represents a pdf. Find an…

A: Introduction: For a discrete random variable X, the probability mass function or probability…

Q: 10. If f (x, y) =2ye” then find √, (x, y). f„,

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Q: Let X1,· , Xn be iid with pdf 1 -(x-01)/02, x > 01, -∞ 0. 02 f(x|01, 02) Show that (Xn – X1)/(X2 –…

A: Given that X1, X2, ...., Xn is iid with PDF, fx|θ1, θ2=1θ2e-x-θ1θ2,   x>θ1 A statistics is…

Q: Exl. suppose the pdf of r.v. X is [x/8, 0<x<4 fx(x)= {*/8, 0<r<4 . Find the pdf of Y =-2X +8. 0,…

A: Y= - 2X + 8, we have dydx= - 2⇔ dx =-dy2and 0&lt;x&lt;4 ⇔ -8&lt;-2x&lt;0 ⇔0&lt;-2x+8&lt;8⇔…

Q: 4. Locate the fixed point of x = xy y = x + y and compute the index about the fixed point.

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Q: 1. f(x) = x² 9 2. f(0) = cos(30) g(x) = 4|x|² 3. f(t) = et cos(ut) 4. f(x) = e³x 9 9 9 g(0) = 12…

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Q: Suppose F′′(x)=Ax+B, with F′(1)=r and F(1)=s. Find F′(x) in terms of A, B, and r. F′(x)= Now find…

A: given  F''(x)=Ax+BF'(1)=r and  F(1)=sF'(x)=∫(Ax+B)dx∫xndx=xn+1n+1+c

Q: 11.7 Let HG and K◄ G, and assume that HNK={e}. Show that if x € Hand y EK then xy =yx.

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Q: 2(x1|x2) = c1¤1/x3, 0 < x1 < x2 < 1, zero elsewhere, and f2(x2) = c2x½, 0 < x sewhere, denote,…

A: *Answer:  Give that 2. Let f12 (12) = C₁x₁/x²2, 0 &lt; x₁ &lt; x2 &lt; 1, zero elsewhere, and f2(x2)…

Q: 5. Find the equation that gives the FT of x,(t) * x,(t) * x,(t) where x,(t) is the rectangular pulse…

A: It is given that

Q: Given y = (u² + 1), u = x² = 5, determine when x = dx - 2.

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Q: Let u(t) = (3,3t,t) and v(t) = (3t, - 2t,2). Compute the derivative of the following function. u(t)…

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