Problem 4. Suppose the PDF of an RV X is fx(t) = √(1-1³) for 0

Q: 13. If f(x) = 1 / (5 + 7x) , find S f(x) by using a u-substitution. Show the u-substitutions.

A: Given, fx = 15 +7x  We have to find ∫fx using u substitution

Q: 11. Suppose f(x)= Y = 4x+1; vilx x = 2, find g(y) u

A: The given probability function is f(x) = x/5, x = 2, 3

Q: Suppose that a PDF for a continuous variable X is given by if 0 x)=3/4

A:

Q: 7. This problem requires calculus. Let P = {a,x" + an–1x"-1 + ...+ a1x + ao | n > 0, ao, . ., an E…

A: Given P is a set of polynomial function of degree n of real co-efficients and a function F:P→P such…

Q: h(x)= Find f(x) such that h(x) = (fog)(x) and g(x)= 10 1-x' f(x) = 10 1-x¹0 10 4 1+x

A: We can solve this as follows:

Q: 2x2 Use the Quotient Rule to find g'(1) given that g(x) = 6x +11 %3D g'(1)=D (Simplify your answer.)

A: Given Data: Function: gx=2x26x+1 The quotient rule of the derivative is, ddxfxgx=gxf'x-fxg'xgx2

Q: 13. Calculate, where Som fx (w > fy (8-w) dw -16 окус). fx (x) = { 1 + 0xxx/ fyl2)= { 0, othmasid. !…

A: Given: fxx=1,0<x<10,otherwise   . . . (1)…

Q: f(x)=8x³ +7x-5-

A: The given function fx=8x3+7x-5. We have to show that the curve does not have a slope tangent 5.

Q: 2- Let a- 0 Ꮎ f(x|0) 1 Find A = MLE(A). 1 6x(x-1) ~~ 2 2x

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Q: Assume that the function f defined by f(x) = 5x+ sin(Tx) is strictly increasing on R and find…

A:

Q: Suppose that f is a function with f'(2) = −5. If u is very very close to 0, then f(2 + u) is…

A:

Q: Question 3 Suppose that f satisfies f (x) dr = 6 and f(r) dr = -4. Calculate %3D 10 – (1)) dz.

A:

Q: Find a function f(x) such that f'(x) = 4x² + 5 and f(0) f(x) = = 3

A:

Q: Q No. 2 Discuss the differentiability of ƒ(x) = (x – 3)' at x = 3 by using definition and…

A: the given function is: f(x)=x-323 we have to discuss the differentiability of the given function at…

Q: c) h(x) =(5x-1) 12x² – 6 d) m(x) = (4x² – 9x} %3D

A:

Q: 15. Find g(1), if g(x)= 2sin-1x

A: The given function is gx=2sin-1x

Q: Find the pdf corresponding to each of the following CDFS: (a) F(x) = (x² + 2x + 1)/16; -1 0.

A: The probability density function can be obtained by differentiating corresponding CDFs.

Q: 1. Employ the following methods to find the maximum of f(x) = 4x – 1.8x² + 1.2x – 0.3x* (a)…

A: Given f(x)=4x-1.8x2+1.2x3-0.3x4. To find: (a) find the maximum using golden search method.…

Q: Iean Value [0, ] is

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Q: Suppose that h(x) = f(g(x)), and that we have the following in- formation about these functions:…

A: Our objective is to find derivative of h at 3.

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

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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: 6. 4 3 1 of 1 2 3 4 5 Graph of f LO

A: The graph of the function f is given and we can see that the above shown graph consists of three…

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

A:

Q: 3. Compute f(x)dx 2x f(x) = { 4 if x < 1 if x 21

A: Evaluating the definite integral by splitting the integral at x=1

Q: 7. Suppose that P (X≥ x) is given for a RV X (of the contineous type) for all x. Find the PDF in…

A: We are given PX≥x for a continuous RV X .

Q: 7. The graph of a function f, which consists of two line segments and a quarter circle, is pictured…

A: As per the Fundamental theorem of calculus, the derivative of the given function  will be given…

Q: 6. If a function f satisfies f(2) = 3, and – 3< f'(x) < 3 whenever 2 < x < 5, what is the range of…

A:

Q: Uniform Random-Number Generator. The typical computer random-number generator yields numbers from a…

A: In the given question , CLT is applicable.

Q: 3. A table of values for the functions f(r) and f'(r) and a graph of the piecewise linear function…

A:

Q: Express the given function h as a composition of two functions f and g so that h(x) = (fo g)(x). 1…

A: Checking all the options.