3.6 Practice Prelim Questions - Review Problems for Prelim...

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Review Problems for Prelim 3Partial DerivativesFind∂f/∂xand∂f/∂y1.x-y22. (3 + 2xy2)33. ln(x2+y3)4.y2ex2y5.x2yx2+y2Find2f/∂x2and2f/∂y∂x6.x4+x2y2+xy3+y47.xy-yx8.xey/xDefinite Integrals (includes Improper Integrals)Volume problems turn into these after you useV=baπf(x)2dx9.2541xdx10.0x(1 +x)-5/2dx11.328x(x2-4)3dx12.212x2+1xdx13.202xx2+1dx14.206x32x2+1dx15.41lnxxdx16.e1lnxxdx17.1e-2xxdx18.0x3e-x2/2dxProbability Density Problems19. A random variableXhas density function 12x2(1-x),Yhas density function 12x(1-x)2.Compute their means and variances. If you do this correctly then the means will add to 1and the variances will be the same, sinceXand 1-Yhave the same distribution.
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Term
Spring
Professor
DURRETT
Tags
Calculus, Definite Integrals, Derivative, Integrals, Variance, Probability theory, probability density function, dx, probability density

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