Let f(x)= (x²e* )/2 for x> 0, and zero otherwise. Show that f(x) is a pdf. b. Find the mean. Hint: It is easier to use the moment generating function.

Q: Compute the derivative of the function F (x) = L evi dt.

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Q: S(r) = In (r² + 2x + 5)

A: SOLUTION-

Q: At what time does f (t) attain its largest value?

A: Consider f(t) is any function. We know that function attains its largest or smallest value when the…

Q: Calculate the derivative e12x d In (t)dt dx using Part 2 of the Fundamental Theorem of Calculus.

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Q: Find the derivative of the function rsin(x) 1- t2 dt. 1+t4 g(x) /1

A: Explanation of the answer is as follows

Q: The fifth derivative of the function f(x) = 5x° is a constar False O True

A: Given query is to find statement is true or false.

Q: What is the approximate derivative of f(x) = x²ex, using backward-difference approach at x=2 and a…

A: The formula for the backward difference is f'x=fxi+1-fxih Now, h=0.1xi=2xi+1=xi+h=2+0.1=2.1fx=x2ex

Q: Differentiate. f(x) = In ( In (8x)) f'(x) = Compute the following derivative using the method of…

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Q: If X has an ex ponential (A) PDF, what is the PDF of W = X² ?

A: 4. Given information: The random variable X has exponential distribution with . The probability…

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of f(2) = / 1 -dt 1+ t…

A: We will find f'(x) as following.

Q: Use the Power Rule to compute the derivative.

A: To compute the derivative using using power rule: ddtt-3t=4. Solution: Power rule of differentiation…

Q: F(x)= ]7+1 3x t dt 2 F'(x) = %3D

A: We will find the derivative using Fundamental Theorem of Calculus.

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y= In (In 5x) O A. 1 5x ОВ. 1 x…

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Q: Find the PDF fy () in the following cases: (A) Y=VX (B) Y = In(X)

A: Given,         f(x)=e-x           x≥0   (A) y=x     dydx=12x⇒dxdy=2x let g(y)  be the pdf of y,…

Q: Verify the statement by showing that the derivative of the right side is equal to the integrand on…

A: We will find the derivative of right side. By showing this derivative equal to integrand the…

Q: Find the indicated derivative. dp for p q² + 2 5q – 3 %3D dq dp dq II

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Q: Find the derivative of the functions below: In(x) (a) g(x) = log,(x) g'(x) = (b). y- in(6x®)

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Q: · F(x) = 5* (S₁²¹6 (√₁+ u²) du) dt

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Q: If X is an exponential RV with parameter A, find the PDF of Y = -14 In(X). 2

A: Given information: If X is an Exponential random variable with parameter λ. The pdf of X is,…

Q: Use the Fundamental Theorem of Calculus to find the derivative of Cos t -dt t11 -3 dy dx II

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Q: Use differentials to approximate V36.1. 3.

A: Consider y = root x.Let take x = 36 and delta x = 0.1.Find delta y as follows.

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative.

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Q: Let f (x) = e10x. %3D Find a formula for the n-th derivative of f, for n 2 1.

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Q: Evaluate the function: S de x(x-2) -dx (x–1)³

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(*) = Ve…

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Q: What is the marginal PDF f(x)? What is the marginal PDF f(y)?

A: The PDF f(x) is:…

Q: The equation of tangent line of the function 36 x3 f(x) e7t dt 36 х at x=1 is Oy- V36 el764 (x-1)…

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Q: Calculate the derivative 12x d dx In (t)dt using Part 2 of the Fundamental Theorem of Calculus.

A: follow next step

Q: dt d Use the Fundemental Theorem of Calculuss to find the derivative dx 1v

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Q: Use the Quotient Rule to show that the Powers of x Rule appies to negative Integer powers. That s,…

A: The given function is fx=1xk   where k>0. Quotient rule says that ddxfg=gdfdx-fdgdxg2.

Q: d rcos t sin(x²) dx dt

A: Given,            ddt∫1cos t sinx2 dx

Q: Calculate the derivative d da 34 dt using Part 2 of the Fundamental Theorem of Calculus. 34 d dx…

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Q: Use part one of the fundamental theorem of calculus to find the derivative of the function. g(x) =…

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Q: Let y = In(x'e2x ). Find dy/dx.

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Q: Determine the equation of the tangent line to the graph of g(x) = | [1- sin(re')] dt at the /In x…

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Q: Calculate the derivative e8x d In (t)dt dæ using Part 2 of the Fundamental Theorem of Calculus.…

A: Given To apply the fundamental theorem of calculus first simplify these integrals so that this…

Q: Evaluate the implicit function by finding dy/dx of x³+3y=3xy

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.  g(x)=…

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Q: Find the derivative of the following function (2t – 1)* dt F(x) = using the Fundamental Theorem of…

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Q: Find the slope of the tangent line to the graph of f(x) 2e'cos-1t dt at x = 1. In x = X'

A: Find the slope with the help of derivative of f(x) at x=1 .

Q: Find the derivative of the following function. y= In (In (4x)) dy dx

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Q: Find the derivative of the function In t dt.

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Q: F(x) = x · S, 2e' cos-lt dt at x = 1 In x

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Q: Find a formula for n.th order derivative of the given functions. 1 b) f(x) = VT 1 a) f(x) = c) f(x)…

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Q: Find the derivative of g(x) = |. •r In z Vt2 +t+1 dt

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Q: Use the First Part of the Fundamental Theorem of Calculus to find the derivative of the following…

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Q: et dt. · e2t 5. Find and simplify the derivative of f(x) = %3D 1 -2 In z

A: Assume g'(t) = e^t/(1-e^(2t))

Q: asin (bvx3 f(x) = c2x + In(kx) if a = 11.23, b= 3, c = 2, and k = 5 at x=1 using CDA with Ax =0.06.

A: We have to evaluate the second derivative of  fx=asinbx3c2x+lnkx at x=1 using central difference…

Q: It follows that the pdf of Y is

A: It is given that the  X has a geometric distribution with parameter p i.e. X~G(p) and fX(x) =qxp ;…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!