Consider the continuous random variable X whose pdf is given by f(2)=√15.50(2). (a) Find the value of k that makes f(x) a pdf. (b) Find E(X). (e) Find V(X). (d) Find P(X ≤ 4).

Q: Find f such that f'(x) = 4x² + 3x-3 and f(0) = 9.

A: (1) f′(x)=4x2+3x−3f(x)=∫f′(x)dxf(x)=∫(4x2+3x−3)dxUsing the Power Rule∫xndx=xn+1n+1+C

Q: A function f has the form f(x) = a + b In(x). Find fif it is known that f(1) = 1 and f(2) = 8.…

A: Find your answer below

Q: (b). Use the definition of the derivative to evaluate f (x)=x". [Hint: Use the Binomial Theorem:…

A: Given: i. fx=xnii. a+bn=an+nan-1b+nn-12!an-2b2+·····+nabn-1+bn. To Find: Use definition of…

Q: TRUE / FALSE) For two pdfs f(x) and g(x), f(x)g(x) is a pdf.

A: Solution

Q: 6 Use the Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 3+x2 (Use decimal…

A:

Q: 4. If fdx = f(x)[In(x) + 1] + C, then f(1) =

A: We have, ∫lnxx2dx = fxlnx+1+C To evaluate : The value of f1

Q: (3) Let X = n(µ,4) and Var(2x) = E(4-7x) find u.

A: Given,X~n(μ , 4)

Q: Let X have a p.d. f.f(x) that is positive at x = -1,0,1 and zero elsewhere. (a) If f(0) =, find…

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Q: Let f(x) = x2 g(x) = 2x-3 h(x) = Vx+1 %3D 5. (go f)(1) 6. (h o g)(5) 8. (f og)(x) 7. (g o h)(1)

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find Give a specific function for F(x). F(x) = = [ x(x² + 6)³ dx F(x) =

A:

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

A:

Q: Find the equation of normal to the function f(x) = x³ - 3x + 1 at its local maximum point.

A: The objective of this question is to find the equation of the normal line to the given function at…

Q: V Find fx) od the bello w function and show that f (f x)) = f°(f(x) =x %3D f(x)= /x+2 -5

A:

Q: 7. f(4) = 34. Find f such that f'(x) = %3D %3D f(x) =|

A: f'(x)=7xIntegrate on both sides∫f'(x) dx=∫7x…

Q: The function f(x) = Ei-1 Cix;| is piecewise linear and convex. True O False

A: Step:- 1 Convex piece-wise Linear: - A function f: ℝn→ℝis a convex piece-wise linear if there exist…

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: Compute f(x)dx f(x) = { 2x if x <1 4 if x 21

A:

Q: Suppose X and Y have the following joint PMF. æ\y_ 1 2 3 4 1/6 1/6 0 1 1/12 1/12 0 1/12 1/12 0 1/6 0…

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Q: Let f(x) = V1+x. Estimate the change in f from x = 7 to x = 7.5 using linear approximation. %3D

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Q: Let 11 f(x) dx = 9, 10 Find "f(e) de = [ and nd S 9f(x) - 7 dx 10 [₁ f(x) dx = 7, [1² f(x) dx = 9.…

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Q: Numerically integrate the following function between a = 0 and b = 10 in n = 12 intervals f(x) = x*…

A: Since you have posted multiple question but according to guidelines, we will solve first question…

Q: Find f such that f'(x) = 4x – 3, f(4) = 0. %3D %3D f(x) = D %3D

A: Given that: f'(x)=4x-3, f(4)=0

Q: 5 Find f such that f'(x) = - √x f(16) = 49.

A: f′(x)=5x,f(16)=49

Q: Consider the PDF f(x) = (1/2)(x+1), -1<x<1 Find the PDF for Y = 1-|X|

A: Probability Theory:Understand the concept of probability, random variables, and probability…