Suppose X has pmf X 013 p(x) .4 2.4 ● Compute E(X). 2 Let h(X) = X². Compute E(h(X)).

Q: 2. . If f(x) dx = 4 and 3g(x) dx = -9, evaluate [² [3f(x) + g(x)] dx

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Q: If ' f(x) = 3 and S. f (x) = 5 , then f (x) =

A: The integral  can also be written as .

Q: suppose f (2) = 4, f ′(2) = 6, g(2) = −1, g′(2) = 3, and f ′(−1) = 5. Give h′(2) when h is defined…

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Q: . Find the inverse of the function f(x) = 1 + (1/x), x* 0. Then show that f(f(x)) = f(f(x)) = x and…

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Q: f(x) dx if Jo Find

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Q: e Gren that f(x) = and g(x) = vx + 5, find the composite function (f gz) a f•g)(x) = 2-7 b. f•9)(x)…

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Q: Given the following table of values: x f(x) f'(x)| 2 -1 -2 5 4 4 x? – 2x – 1 - A. If g(x) then g'…

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Q: πχ If f(x) = 1 + x³ + tan 4 find (ƒ-¹)'(3)=?

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Q: Let f(x) = 6x3 and g(x) = x² – 8. Compute the following functions. 1. f(g(x)) = | 2. g(f(x)) = 3.…

A: The functions are given by fx = 6x-3 and gx = x2-8 To determine: The expression of the following…

Q: 4. Given a function f(x) that is written as f(x) = h' (2) = 4, then f'(2) =? g(x) h(x), if g(2) = 2,…

A: 4. Given a function f(x) that is written as f(x) =g(x)·h(x) , if g(2) =2 , h(2)=-2 ,g'(2)=-3 and…

Q: Let f(x)= x², g(x)= 2x+5, and h(x)=x² –1. Find each. 9. h[S(-2)]= 10. S[g(x-1)] =, 11.

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Q: 6. Find [ f(x)dx if f(x) = et -1, if -3<x<0 V9-x², if 0<x<3

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Q: - Find E f(x) dx if [3 for x 3 f(x) =

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Q: Let f(x) = 8+ Væ – 4. Find f-'(x). f-1(x) = Now for fun, verify that (f o f-1)(x) = (f-1o f)(x) = a…

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Q: 8. If f(x) dx = f(x) + C, determine f(x). Justify your answer. %3D

A: Given, ∫f(x)dx=f(x)+C Differentiate both sides with respect to x, we get f(x)=dfdx…

Q: 3. Compute f(x)dx (6 points) f(x) = { 2x if x <1 4 if x21 %3D

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Q: Suppose f(x) = x² In(x). then f"(e) equals

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Q: If f is a positive function and f"(x) < 0 for a < xs b, show that T, < f(x) dx < M,

A: f is a positive function and f''(x)&lt;0 for a≤x≤b This tells us that f is concave down over the…

Q: Let {X} be i.i.d. such that X₁~ Pa(4, 1500) and suppose that N(2) ~ Po(100). Find E[S(4)] and…

A: Given that  be iid. such that  and

Q: Find the function f(x) such that f'(x) = f(x)(1 – f(x)) and f(0) = (Use f for f(x) in your…

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Q: Suppose f(x) > 0 on [0, 3], f(z) <0 on [3,7), f(z f(x) dr = 5, and f(x) dx = -9. Evaluate (0). re…

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Q: Determine Rn(x) for f(x) = 1ln(x) about x = e

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Q: Given g(z) = In(5z+), the derivative g (z) is. %3D O 42 O 5z +z O 20z +1 O 20z +1 5z4 +z 5z +I 20z+1

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