1. Let X1,. , Xn be iid N(0,0), and Y = E X}/n. ... (a) Find EY. (b) Find Var(Y).

Q: Co. If FCx)=3x-4,+4+1,finelf(xland f"(x)

A: To find out f'(x) and f"(x).

Q: 3x-4 -,x < 1 x+2 4. Given the function f (x) = . Calculate f'(1-) and f'(1+). In?x x+1

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Q: Let f(x) = 2x e¯x*,x > 0 and Let Y x2. Find G(y)and g(y). %3D

A: In this question,  we need to transform the variable in the probability density function.

Q: Let h(x) -222+z+4 %3D ,what is h' (-5)? 2+4z-1

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Q: 2x2 - бх + 5 |Let f(x) = Evaluate f' (x) at x = 1. 4x2 + 3x + 10 f'(1) =

A: Given: f(x)=2x2−6x+54x2+3x+10 Quotient rule of differentiation states that ddxfg=f'g-g'fg2

Q: If f(x) is continuous on (-15,-5)such that, -10 SI5 f(x)dx=13 and/" f(x)dx =6 then find f(x)dx -10…

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Q: (x. v) = (0, 0)

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Q: +4x –1 dx x' - x 2.

A: As per our guidelines we can help you in solving only first problem rest of the problems you have to…

Q: Suppose X,~ Uniform(0, 2) and X, ~ Uniform(0, X,). Find E[2X,+X,].

A: Given,X1 ~U(0,2)X2 ~U(0,X1)E(X1)=2+02=1E(X2)=X1+02=X12

Q: Let 7(t) = VE + 4, cos(t), te-'> (t*), te¯t >

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Q: Let F(x) =Cx41D, fCx)=X,and gox)=x+1 True or fals e (gof)(x) = FCX).

A:

Q: Given f'(x) = 3x4 — 4x³ + 7. Find all critical numbers of f'. (a.) 1 and 2 (b.) 1 and 3 (c.) 0 and 1…

A: To find the critical numbers of f'

Q: 4. If /(r.y)=- , find f, and f,. V+y

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Q: y² + 1/²2-44 = = =-=-66 et +2 a) y (-1.5) = 1.7 b) y (8)= -3.14 determine the largest interval a…

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Q: 4. Find f"(2). (a) f(u) = 2u²5 – u).

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Q: Show that Var (Y) = Var(ε₁) = 0².

A: Let us consider a simple linear regression. The equation of a simple linear regression model is:…

Q: Let X ~ Gamma (8, 2) . Then E |[X²] is equal to

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Q: Given f(z) 3D 1-홀 (7+ 3x) + 을(7+ 3x)2- (7+3x)" then f'(z) =. -을 + 꼴 (7+ 3z) -(7+3x)2+ | .... -글 +…

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Q: Let f(x) = e*. What is f' (3)?

A: Differentiate wrt x

Q: Is |3x-1| a function?

A: A relation is said to be a function only when every point in the domain has a unique value in the…

Q: Let X ~ T(a, B). If E(X) = aß and E(X²) = aß² + a² ß². If â = X, find the method of B moments…

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Q: Let f(x) = x³ + √√. Then f'(1) = 02 O 1.5 O 3.5 04

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Q: Let f(x)= x³+1. Then (fof)'(1)= O 20 O 36 O 3 O 9

A: Please refer to the image below

Q: 3. Suppose that f(1) = 2, f(4) 7, f'(1) 5, f'(4) = 3, and f" is continu- %3D | af" (x) da. ous. Find…

A: The given data is: f1=2f4=7f'1=5f'4=3  f'' is continuous  To find the value of ∫14xf''xdx.

Q: Given f (x) = x³ - 3x – 1,x 2 2, find (f~')'(-1)

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Q: Let f(r) = 3x² + 4x + 5 = (x),f f'(1) =

A: To find the derivative