3. The density function of X is given by f (x) = {"" Sa + bx2 0 < x<1 otherwise If E[X] 2 find a and b.

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A: Find the anti derivative.

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A: Let, y1,y2,...yn be random sample from the exponential pdf with unknown parameter λ. Now, to find…

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A: given       ∫0lnln8∫y=exln8exeydydx=

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A: Given that Φ(x,y) = ex-y and Φ(ln2,ln2)=1. Now by using the technique of linear approximation we…

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Q: (11) When the conditional density of X given Y = y E (0, 1) is 2x fx|Y=y(x) = y < x < 1. 1- y2…

A: We have to solve given problem:

Q: 6. Let a be a positive constant. Determine the general antiderivative of a using the fact 1 a² + x2…

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Q: Give the antiderivatives of e-x.

A: ∫e-x dx

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A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

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Q: [8] 3. In a process of sintering(heating) two types of copper powder, the density function for Y1,…

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Q: hoaph fumeten nd be fure at label aut least thne f (u) : Su

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A: Here we use substitution so simplify the integration.

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Q: (11) When the conditional density of X given Y = y E (0, 1) is 2x fxjY=y(x) = y < x < 1. 1 – y2 '…

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Q: Example 17-23. Prove that under certain general conditions of regularity to be stated clearly the…

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Q: 2. Evaluate. th fallowing.integrals.a.fte..seueo.ing.the arder.af.integratren. dyd x Ans..In7)4…

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Q: If the change of variables u = x + 1 is used to evaluate the definite integral f(x) dx, what are the…

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Q: QUESTION 7 w the joint dernsity af Xy and X2s gven by ** for 0<X<2,0< x2<2,0<x + X<2 ehsewhere find…

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Q: X and Y are exponentially distributed and independent with densities f(x)=-exp| a a X Obtain P X +Y

A: 8. From the given information, X and Y are exponentially distributed and independent.…

Q: #3. Suppose that h(x) is integrable and that ,h(x)dx=1 and S,h(t)dt = 6. Find a. Sh(x)dx b. –…

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Q: 1-cos(x) X has PDF f(x) = if 0 < x <T 0 otherwise %3D Find the probability P(0.38 < X < 3.12).

A: Given:fx=1-cosxπ, if 0&lt;x&lt;π.fx=0, otherwise. The probability, Pa&lt;x&lt;b  of a probability…

Q: 3. The integration of x e* with respect to x is: A. e2x. В. 2хе* С. 2

A: To integrate  xex2 with respect to x: ∫ xex2dx Apply u-substitution: u=x2 Differentiate both sides:…

Q: 8. The y coordinate of the centroid of the plate (uniform density) formed by the curve f(x) = e and…

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Q: 2. Find the temperature distribution inside a solid parallelepiped with sides (a, b, c) whose faces…

A: Here, uxx + uyy +uzz = 0                                  .......1 with conditions, ux,y,z,0 = A…

Q: 3. f(x) = _-x² +1_ %3D 9- x + zX Holes: Vert. Asy: Hor. Asy: x-int: y-int: Domain 4. f(x) = x3 – x2…

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Q: In z 25 If the triple integral So" Sõ So™² (xe¯y) dydx dz Find the upper limit value E.

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Q: 9. Let f(x) x In(10) Find the most general antiderivative. F(x)

A: Given data÷ So,we need to find F(x).

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

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Q: Can you help me step by step?

A: dA/dt may be written as,

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Q: Problem 11 The volume of the solid obtained by rotating the region enclosed by  y=(x^2), y=6x,…

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Q: b) Find the maximum and minimum values of the function u(x, y) = e' cos x throughout the region {(x,…

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Q: Let f(x) = 9 · 5" ln(5). Find the most general antiderivative. F(x)

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Q: (11) When the conditional density of X given Y = y E (0, 1) is 2x fx\Y=y (x) = 1 – y² y < x < 1.…

A: We know that  EXY=y=∫xfXY=yxdx Now, we have fXY=yx=2x1-y2, y&lt;x&lt;1…

Q: a) the linear approxinma ion to the function + 3X ät

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Q: 3. Estimate the integral v2 + x² dx using appropriate of Simpson's rule with step size, h = 0.2.

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Q: 3

A: Given Joint Density function

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A: Please check step 2 for solution

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Q: 10. Find the minimum of the integral I[y] subject to the constraint TIy) = [, s° dx = 2 JL over all…

A: Consider the problem: Extremize I[y]=∫x1x2F(x, y, y') dx subject to J[y]=∫x1x2G(x, y, y') dx=L ,…

Q: (13) For the conditional density given in problem (11) above obtain Var(X|Y = y) for y E (0, 1). The…

A: 13. From the problem 11, fx|Y=y(x)=2x1-y2, y&lt;x&lt;1 Consider, EX|Y=y=∫xxf(X|Y=y)dx…