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Xcxy vs. If Y = eX nd the pdf of Y Note Y it is said to have a lognormal distribution Example 3 Let Xbe a continuous random variable with pdf f(x) = 2(1 x);0 x 1 If Y = 2X 1 nd the pdf of Y Example 4 Let Xbe a continuous random variable with pdf f(x) = 3 2 x2;. 21 x 1 If Y = X nd the pdf of Y 11 Continuous random variables Some examples (Some are from Sheldon Ross (02), A rst. Y V s ɏo X ΊC O ̔ \ Ȃ Ƃ͂ m 낤 H @ y V C O ̔ ̃g b v y W ͉p A A ؍ Ɋ S Ή B e V b v i y W Ȃǂ Google ɂ 24 ɖ ܂ B z 121 ɑΉ \ B C O ̔ { i I ɍl ꍇ ̑I ̈ Ƃ Ċy V s ֏o X A u y V C O ̔ v ̂ ł́B Ⴆ ANHK ́w J C CTV x ŕ f Ă ̂ł A A W A E b p E k ĂȂǂ̓ { ̃t @ b V D ̏ ̎q ́A y V Ńt @ b V t @ b V G w Ă ƌ Ă ܂ B y V o X Ɋւ Ă͂ >>.
X,Y = Cov(X,Y) WhenCov(X,Y) > 0, X andY aresaidtobepositively correlated, whereaswhenCov(X,Y) < 0, X and Y are said to be negatively correlated When Cov(X,Y) = 0, X and Y are said to be uncorrelated, and in general this is weaker than independence of X and Y there are examples of uncorrelated rvs that are not independent Note in passing. Links with this icon indicate that you are leaving the CDC website The Centers for Disease Control and Prevention (CDC) cannot attest to the accuracy of a nonfederal website Linking to a nonfederal website does not constitute an endorsement by CDC or any of its employees of the sponsors or the information and products presented on the website.
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