Statistics Equation Sheet for MSC 287 - Dr. Stafford, Study notes of Business Statistics

Download Statistics Equation Sheet for MSC 287 - Dr. Stafford and more Study notes Business Statistics in PDF only on Docsity! EQUATION SHEET FOR MSC 287 - - Dr. Stafford Freq Dists: ri = fi/n %fi = 100(ri) cfi = cfi-1 + fi {f0 = 0} crfi - crfi-1 + ri = cfi/n {crf1 = r1} %rfi = 100(crfi) 3fi = n 3ri = 1.0 Histograms: K . log(n)/log(2) Width . range/K Pie Charts: osector = 360(ri) Location: Median: n odd, p = (n+1)/2 & Med = Xp; n even, Med = (Xp + Xp+1)/2X X n= ∑ / pth %tile: i = (p/100)n; i not integer, round up and Pp = Xi; i is integer, Pp = (Xi + Xi+1)/2 Q1 = P25 Q3 = P75 Variability: Range = Max - Min IQR = Q3 - Q1 MAD = ( ) /X X ni −∑ Variance: Std Dev: CV = [ ]s X X n n 2 2 2 1 = − − ∑∑ / s sX X= 2 ( / ) *s X 100 Relative Location: Chebyshev: (1 - 1/z2) within z dev. Of meanZ X X si= −( ) / Association: Covariance: Correlation: ( )( ) s XY X Y n nXY = − − ∑ ∑ ∑ / 1 r s s sXY XY X Y = Counting rules: K-step experiment: (n1)(n2)...(nK) combinations: n xC n x n x n x =       = − ! !( )! Laws of Probability: 0 # P(Ei) # 1 3P(Ei) = 1 P(A) + P(AC) = 1 P(AcB) = P(A) + P(B) - P(A1B) P(A1B) = P(B)P(A|B) = P(A)P(B|A) Independence: P(A|B) = P(A) Or P(B|A) = P(B) P(A1B) = P(A)P(B) Mutually Exclusive: P(A1B) = 0 Bayes’ Theorem: , K = # classesP A B P A P A P B A P A P B Ai i K K ( | ) ( ) ( ) ( | ) ... ( ) ( | ) = + +1 1 (1) (2) (3) Given (4) = (2)(3) (5) = (4)/P(B) Events, A1 Priors, P(Ai) Conditionals Joints P(Ai1B) Posteriors P(Ai|B) A1 P(A1) P(B|A1) P(A11B) P(A1|B) A2 P(A2) P(B}A2) P(A21B) P(A2|B) Totals 1.00 P(B) 1.00 - - - - - - - - -- - - - - - - - -- - - - - - - - -- - - - - - - - -- - - - - - - - -- - - - - - - - -- - - - - - - - -- - - - - - - - -- - Discrete Dist. µ = E(X) = Σ[X P(X)] σ2 = VAR(X) = EX2 - [E(X)]2 = Σ[X2 P(X)] - {Σ[X P(X)]}2 {solve with table} Binomial Dist. , X = 0, 1, ..., n E(X) - np VAR(X) = np(1-p)f X C p pn X X n X( ) ( )= − −1 Poisson Dist. , X = 0, 1, .... E(X) = λ VAR(X) = λ λ(t2) = (t2/t1) λ(t1)f X e XX( ) != −λ λ Uniform Dist. f(X) = 1/(b-a), [a < X < b] E(X) = (a+b)/2 VAR(X) = (b-a)2/12 p[u < X < v] = (v- u)/(b-a) Exponential Dist. f(X) = (1/µ)e-X/µ , 0 < X < 4; E(X) = µ VAR(X) = µ2 P[0<X<v] = 1 - e-v/µ P[X > v] = e-v/µ P[u < X < v] = e-u/µ - e-v/µ Normal Dist. , -4 < X < +4 E(X) = µ VAR(X) =f X e X( ) ( ) /= − − 1 2 2 22 πσ µ σ σ2 Standard Normal E(X) = 0 VAR(X) = 1 Use table to read probabilities {7 models all convert to Model I} Sampling Dist of E[ ] = µX X σ σX n= / or For n/N $ 0.05 ( ) ( ) ( )[ ]σ σX n N n N= − −/ / 1