1. Suppose that X1, X2, · · · , Xn are iid (independent and identically distributed). Let E[Xi ] = μ and var(Xi) = σ^2, where i = 1, 2, · · · , n. (a) Find E[X]. (b) Find Var[X].

Q: Let r(æ) = f(g(h(x))), where h(1) = 3, g(3) = 2, h'(1) = 9, g/ (3) = –2, and f'(2) = 5. Find " (1).…

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Q: Let F(x) = f(f(x)) and G(x) = (F(x))² and suppose that Find F'(8) and G'(8). = F'(8) = G'(8) = ƒ(8)…

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Q: Differentiate the following function: VP - 4V U = u =||

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Q: If f(x) + x²[f(x)]³ = 10 and f(1) = 2, find ƒ'(1). f(1) = 10 X Type here to search

A: I am attaching image so that you understand each and every step.

Q: (f) p(xj,...X) =E

A: Degree is n.

Q: Suppose that the p.d.f. of X is as given f(x) = 3(1-x)2 for 0<x<1 and 0 otherwise Find the pdf of…

A: If Y=g(X) is the transformation then the PDF of Y is given by; fY(y)=fX(g-1(y))ddyg-1(y)

Q: if y= x/lnx then find y`

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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: Differentiate the function In e* 8.) y = ex 7.) f(x) = e** – In :

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Q: Evaluate SIL. dydzdke, where E = {(x,y,z): (2+z12<x< 2, - (4 - z)2sy <(4 -2)12, 3<z 58}.

A: Given: The given integral is ∫∫∫Rdydzdx The given intervals are (y2+x2)12≤x≤2, -(4-z2)12≤y≤(4-z2)12,…

Q: Compute f(s), where f(x) = cos oz and 8 >

A: We have to find out the Laplace transformation of f(x) = cos

Q: b. foet t'dt

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Q: Let Ximexp (A). Show i Sulficieny that T-ZXi is Statistics

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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: If X~BET(1,2) then E(X)= (1 2/B (1/B

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Q: Suppose that Var(X) = 879.05, Var(Y) = 8681.72, and Cov(X,Y) = 2281.58. What is Var(.08X + .92Y)?

A: The objective of the question is to find the variance of the linear combination of two random…

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

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Q: let p(x)=g(f(x)). use the given table to find p'4

A: p(x)=g[f(x)] diff. w. r. to x p'(x)=g'[f(x)] . f'(x)  ..................(1)

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

A: Differentiate wrt x

Q: f(1) = 4x'/^(z' - 3). Evaluate the following specific values of f': (A) f' (1) = (B) f' (6) = %3D

A: Given that f(x)= 4x13x3-3 we have to find the derivative of f . To find the derivative we use power…

Q: Suppose that f and g are functions such that (0) = 4, f'(0) = 5, g(0) = –2, gʻ(0) = 3. %3D æf(x)…

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Q: Suppose that f(x) = x2 + 17 Find f' (1). f'(1) =|

A: The function fx=exx2+17. We have to calculate the value of f'1.

Q: Find f such that f'(x)=x² +4 and f(0) = 1. f(x) =

A: NOTE: Refresh your page if you can't see any equations. . take integration on both sides

Q: f(x) = ex/³; [1₁3]

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Q: Suppose that P(A') = 0.3, P(B) = 0.8, P(A U B) = 0.9. Find P(A), P(An B), P(An B') and P(A'|B).

A: We have given that P(B) = 0.8 We have to find P(A),  and

Q: Evaluate f'(x) at x =2 given f(x) = ÷(x² - 3)*

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Q: If you are asked to find L4 for f(x) = edz) + In(x) on the interval [2,10], what would the value of…

A: From the given problem:   fx=e3x2+lnxa,b⇒2,10   As we know that the expression for the step size is:…

Q: Let f(Wx)= 6x. Then f' (2)= %3D 12/2 1 12 12 24 - 12 6.

A: The given function is: fx=6x