(a) Show that e-x² dx = JT, and deduce that 1 exp { (x - )2 202 f(x) = -00 < x 0. Provide a detailed solution

Q: Recall that the gamma function is defined by the integral T(a) = ta-le ta-le-t dt, a > 0, and, r(a…

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Q: u2 and ult) ond Ret) ore both diffrentioble %3D functions. Iff uc8) =3 , K(1) = 2, U'I2) =5,…

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Q: Show that+ = 0, %3D ax dy? where f(x, y) = In(x² + y²) + tan¯'(²) %3D

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Q: The joint pdf for X and Y are given as: f(x,y) = {6x^2; 0<x<1 , (1/3)x<y<x 0; ew] (i) Find E [Y…

A: The joint pdf for X and Y are given as:

Q: Let f(x) = 6 – x j'(z) = Preview

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Q: 2. Suppose a thin wire with linear density 8(x) = ln(2x) lies between x = 1 and x = 3. Find the mass…

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Q: X = Xo Give an example of a function f such that the derivative of Så fl+dt at does not equal f(xo).…

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Q: Calculate S (xyz) dz dy dx. (x=1 cy=1-x cz=2-x x=0 Jy=0 Jz=0

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Q: = In ( ²² +2²³v-_-²³ ) · then x +y is da by x-y If the function u = ln

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Q: Where is the function f(z) = Log(z2 + 1) holomorphic? What is its derivative in the region where it…

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