Problem 4 (1) For X k=0 Binomial(n,p), prove formally that E(X) = Σ‰± kP(X = k) = np and Var(X) = np(1 − p). (2) For T~ Geometric (p), prove E(T) = 1/p. ~

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

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A: Differentiate the following:   F(x)=(6x+1)2

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A: Using formula of slope of tangent &amp; integration to find f(x)

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A: Given: y=e−x.lnxShow  that:x2d2ydx2+dydx+e−x(1+x)=0

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A: ∫x+ex2dx

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A: Here, Definition of Gamma function is ∫0∞e-ttx-1 dt= Gamma(x).

Q: d? 9. If g(1) = 2, g'(1) = 3, g"(1) = -1, S'(2) = 4, and "(2) = 3, then %3D

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