Stat Formula Sheet

Stat Formula Sheet - Poisson f x = Gamma f x = Weibull 1 e...

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Unformatted text preview: Poisson f ( x ) = Gamma f ( x ) = Weibull 1 e x / = -x , =failure rate, =time to failure = = 1/, 2 = 2 = 1/2 e ( r ) ( x ) r -1 e -x , =failure rate, r = # failures =r/ 2 = r/2 f ( x) = x -1e- x , = avg. time to failure, = shape parameter, x = time to failure = -1/ (1 + 1/ ) 2 = -2 / (1 + 2 / ) - 2 If X is binomial and np and n(1 p) are both 5, then X is approximately normal with = np and = npq. Hence, z = X - = X np is standard normal. npq Discrete Continuous P(X=18) P(17.5 < X < 18.5) P(X > 18) P(X > 18.5) P(X < 18) P(X < 17.5) P(X >=18) P(X > 17.5) P(X <= 18) P(X < 18.5) Linear Relations 1 r +1. r > 0 indicates a positive (x inc. / y dec.), r < 0 indicates a negative (x inc. / y dec), r = 0 indicates no relationship r= SS ( xy ) SS ( x) SS ( y ) SS ( x) = x 2 ( x) - n 2 SS ( y ) = y 2 ( y) - n 2 SS ( xy ) = xy - x y n Least squares reg. y = bx+a B = Joint density SSxy y x A= -b SSx n n f XY 1) f XY (x,y) o 0 2) (x,y)=1 3) P(a f X X Y b and c Y d) = f ( x, y )dydx XY a c Y X b d Independence 2 f XY (x,y)=f X ( x ) fY ( y ) 2 yf xf and cov = 0 E [ X ] = XY ( x, y )dxdy E [Y ] = XY ( x, y )dxdy Y X Var(x) = E(x ) [E(x)] Cov( X , Y ) = E[ XY ] - E[ X ]E[Y ] Cov ( X , Y ) fxy ( x, y ) fxy ( x, y ) Pearson Correlation = fx|y= fy|x = XY (VarX )(VarY ) fy ( y ) fx ( x ) x | y = E ( x | y ) = x * f x | y dx y | x = E ( y | x) = Density y* f x - y| x dx f ( x) = 1 2 x e x- -1 2 2 Cumul. Dist. Func.= f (t )dt Expected Value E ( x) = xf ( x)dx, E ( x 2 ) = x 2 f ( x)dx x ...
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