7. (25 points) Let X have the pdf f(x) = 2, -2 < r < 4. Find the pdf of Y = X² using Two-to-one function technique.
Q: 9. State the Second Derivative Test for functions of two variables z = f(x, y)
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Q: Q2/ A/ Show that the functions f(x) = sin-1() and g(x) = 2tan-Vx, have the same derivative. %3D
A: Given : f(x)= sin-1 ( x-1 / x+1 ) g(x) = 2 tan-1 (√x)
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Q: 1-x Find the derivative of y = arctan %3D 1+x
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Q: If X and Y have joint pdf given by
A: From the given information, fX,Yx,y=2I0,yxI0,1y =2, 0<x<y, 0<y<1
Q: find the derivative of y with respect to the appropriatevariable. y = csch-1 (1/2)θ
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Q: 4. Write a script which uses finite difference approximations to compute the first derivative dy/dx…
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Q: Use forward-difference formula to evaluate the first derivative of y = tan(x) at x = 1 using a value…
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Q: 4)* Find the derivative of f(x)= Arcsecr. %3D f'(x) = 4 rv.r* O None of the above O Option 4 f"(x)=:…
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A: topic - slope of curve note - As per bartleby guidelines ,we are supposed to answer only first…
Q: fcx)= Y文 メ ー^
A: Local extrema
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Q: # 5) Find the extrema points for the function f (x) = using the second derivative tes 1+x x2 %3D Fon…
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Q: 2. Find the derivative of f(x). (a) f(x) = x² sec x (b) f(x) = 1+ tan a 1- tanz
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A: On solving this we will get
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Q: Can you help me step by step with this problem?
A: Given,
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A: Using chain rule of differentiation.
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A: We have to find the derivative of the given function.
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Q: find the derivative of y with respect to the appropriatevariable. y = sec-1 (2s + 1)
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Q: e derivative of y with respect to x. y= 2sin^-1(5x^4
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Q: find the derivative of y with respect to the appropriatevariable. y = csch-1 2θ
A: Given, y=csch-12θ
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A: see below the answer submit the q12 with what to do with the question
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A: Derivative of the function using definition
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Q: 5)Let f ( x ) =3x4 + 4x3 Find the derivative. b)Find the critical numbers.
A: Given problem:- 5)Let f ( x ) =3x4 + 4x3 a) Find the derivative. b) Find the critical numbers.
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- Let X1, X2 denote two independent variables, each with a x^2(2) distribution. Find the joint pdf of Y1=X1 and Y2 = X2+X1. Note that the support of Y1, Y2 is 0<y1<y2<infinity. Also, find the marginal pdf of wach Y1 and Y2. Are Y1 and Y2 independent?X has the uniform distribution [0,1] Put Y=2x + 5. If f(x) is the pdf of Y then f(x) = ?Let x and y be joint continuous random variable with joint pdf f XY (x, y) = {?x + 1 , x, y ≥ 0, x + y < 10, ??ℎ??????1. Find the constant c.2. Find the marginal PDF’S fX (x) and fY (y)3. Find P(Y<2X2)
- Let X1, .... Xn be a random sample from a population with location pdf f(x-Q). Show that the order statistics, T(X1, ...., Xn) = (X(1), ... X(n)) are a sufficient statistics for Q and no further reduction is possible?Assume that X1, X2, X3 ∼ Exp (λ) are independent and evenly distributed with the distribution Exp (λ = 1). (a) Determine the distribution of Y = X1 + X2 + X3 and state its PDF f (y). (b) Determine the distribution of U = 2YLet f(x) = ½ , -1 < x < 1 0 otherwise be a pdf of the random variable X. Find the distribution function and the pdf of Y= X2
- 4- Distribution of velocity (DV) of a molecule is given with the following equation a, b, e, D are constants. Find the the most probable velocity where DV is at maximumThe point pdf of the random variables X and Y is pictured: a) Find the marginal pdf fx(x) of X and the probability P(X≤0.5) b) FindE(X), E(Y), E(XY) and Cov(X, Y).Q4) If X is a continuous random variable having pdf ke~ (2x+3y) x>0y>0 xy) = = e p(x) { 0 otherwise Find a) the constant k b) P(X>1) ¢) X, X2, 02, standard deviation.
- LetX1,X2,...,Xn be a sequence of independent and identically distributed random variables having the Exponential(λ) distribution,λ >0, fXi(x) ={λe−λx, x >0 0, otherwise Define the random variable Y=X1+X2+···+Xn. Find E(Y),Var(Y)and the moment generating function ofY.f X1,X2,...,Xn constitute a random sample of size n from a geometric population, show that Y = X1 + X2 + ···+ Xn is a sufficient estimator of the parameter θ.A continuous random variable X has the PDF fx(x)=kx2, 0 < ? < 1.a) What is the value of k ?b) Find the variance of Xc) What is the value of m so that P[X<=m] = 1/2 ?d) Find the PDF of the new random variable Y obtained from X through the lineartransformation Y=4X+1.