2. Suppose that p(x) = 1/5, x = 1, 2, 3, 4, 5 is the pmf of X. Find (a) E(X) (b) Var(X) (c) E [(x + 2)²]

Q: Which of the functions g(x) are such that 4" is (g(x))? (Select all that apply.) Og(x)=2+3+4 Dg(x) =…

A: Solution 5 : the correct options are : A and E Solution 6 : the correct options are : A

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

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Q: Suppose 4 0 2 8 * (3f(x))dx = 12 and -2 d[ f(x)dx = 2. Compute 5 5 -2 f(x)dx.

A: NOTE: Refresh your page if you can't see any equations. . here we have and

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: Suppose that f(r) = 5x/5 – 2x5/7. Evaluate each of the following: f'(2) =| f'(6) =| %3D

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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: x (e) / Int √x dx

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Q: Find a formula for f(") (x) if f(x) = e-10: fln)(z) =[]

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Q: 5. Which is the inverse of f(x) =2? %3D Or (2) = H 241 Of (x) = 1- Of (x) = 1 1-c f(x) = 1+a

A: To find f-1(x) We interchange x and y and solve for y as function of x

Q: 15. (1.3.36) Find fogoh, where f(x) = |x4| g(x) = 2x h(x) = √(x)

A: To find , where

Q: Let f(x) = 3x + 1, x, = -1, x, = 0, x3 = 1, x4 = 2, and X5 = 3. Find E f(x,).

A: we have the given the following details   f(x)=3x+1x1=-1x2=0x3=1x4=2x5=3We have to find∑i=15f(xi)

Q: Suppose that F'(x) O... = 8+4ln(3/5) O... 16+4ln(5/3) = O = 8+2ln(3/5) O 16ln(5/3) = x X 2 Then F(7)…

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Q: Show that E(X-µ)³ = E(x³) −3 [E (x²) ][E(X)] + 2[E(X)]³

A: The linearity of expectation property: With the assumption that, Xi's (i=1,2,...n) with n positive…

Q: 4. Let f(x)= |x| and g(x) = x-3. (a) Determine the formulas for each of the related composite…

A: The composite function is defined as when the output of one function is used as the input of another…

Q: a. Choose the proof that shows f(x) = x1 and g(x) = Vx are inverses of each other below. OA. f(x) =…

A: To Determine: Given both functions are inverse of each other.

Q: 14. Given the functions f(x)=x +1, g(x)=/2x and h(x)=- x+3 find: %3D a) f(8(9)) b) f(8(x)) c)…

A: Given  f(x) , g(x) and h(x)

Q: 9. If (x-1)/(x) 3x²45x-2 X x²+2x 2x²-x-1 x² g(x) 6x²+x-1 find a relationship between f(x) and g(x).…

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Q: 1 - f(x) = =+ X 1 x+1

A: Our Aim is to solve f(x)=1x+1x+1-(i)

Q: D) Identify the even function among the following. A) f(x) = 2|x| - x² %3D B) h (x) = 2x – x² %3D C)…

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Q: Acar battery has a range that follows an approximately Normal distribution with mean 700 km and…

A: Given, X~N( 700,442 ) n=31 sample mean=690

Q: By using Rodrigue's formula, prove the following relation Ph+1(x) – Ph-1(x) = (2n + 1) P,(x) 4- %3D

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Q: Expected value  b Variance c Standard Deviation

A: Here prepare probability table with required column

Q: 1. Given f(x) = x +3x-4 and g(x) = x- 1, x 1, find (x). A. x + 4 O B. x + 3 C. x+2 D. x +7

A: Given data is : fx=x2+3x-4 and gx=x-1 , x≠1   To find the value of fgx

Q: 10. Determine all x E R such that [x] + Lx + = [2x]. %3D Justify your answer.

A: Given that x+x+12=2x    x∈R        - (1) Case - (i) Let x is an integer i.e; x=m Then from equation…

Q: 2. Given f(x) = x' – x? - 5x – 3. which of the following is a factor of f(x)? 1. x - 2 2. x+ 2 3. x…

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Q: 1. If f(x) = x/(x − 1) and g(x) = 3/(x² − 1). Find the value of x for which (f + g)(x) = 1

A: Solving the problem

Q: 33. Find [g of ]x when f(x) = 2x + 4 and g(x)=x²-3x + 2. a. 4x² + 10x + 6. b. 2x² - 6x +8 c4x² + 13x…

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Q: If s(0)=−4, s(7)=−5, f(0)=2, and s′(x)=f′(x) on [0,7], determine the value of f(7)? (Do not include…

A: We have to determine the value of f7  given,  s0=-4, s7=-5, f0=2 and s'x=f'x on 0,7 Since, s'x=f'x…

Q: Find f (x). f(x) = 2 In (1 + 7x?) f(x) = %3D

A: f(x)=2ln(1+x2 ) Differentiating w.r.t x both sides, we have f'(x)=2ddx (ln(1+x2))…

Q: Let f(x) = 3 + 2(x-3) + 0(x-3), as x→3 and let g(x) 2 B. g (3) = ² 3 ·g is defined and…

A: We will find the required.

Q: d. Compute E(X) and Var(X).

A:

Q: -Vx2+5 -x f(x): f'(0)? -x+2

A: