Midterm Formulas and Help sheet

Formulas (4.1) Classical method of assigning probabilities (4-2) Mutually exclusive events X and ¥ (4-3) Independent events X and V' (4-4) Probability of the complement of A (4.5) Counting rule (4-6) Sampling with replacement (4.7) Sampling without replacement (Combination) (4-8) Permutation (4-9) General law of addition (4-10) Special law of addition (4.11) General law of multiplication (4.12) Special law of multiplication (4.13) Law of conditional probability (4.14) Bayes'rule P(X|Y) = P(XNY)=0 P(X|Y) = P(X) and P(Y|X) = P(Y) P(A) =1~ P(4) ] n! aPr Tl P(XUY)= P(X)-P(Y)-P(XNY) P(XUY)= P(X) +P(Y) P(XNY)= P(X)-P(Y|X)= P(Y)-P(X]Y) P(XNY)=P(X)-P(Y) PXNY) _ PX)PYIX) PEY)= P(Y) P(Y) P(X:)-P(Y]X:) P(X;)-P(Y|X1) + P(Xs)-P(Y|Xs) +---+ P (Xa)-P(Y]Xn)

Formulas (3.1) Population mean (3.2) Sample mean (3.3) Interquartile range (3.4) Mean absolute deviation (3.5) Population variance (3.6) Population standard deviation A _ Z':z:,- PN 7= 2% on IQR = Q3 — @ 2 |z; — #I MAD = ~ o2 Y(mi — ")2 N N (Em.g)z Yl — o2 = ' N N 2 Ya? — Np? B N o = ol y — (2 —u)? N N (23:,)2 Yt — o = \' - N N . Ya? — Np? B N

(3.7) Chebyshev's theorem (3.8) Sample variance (3.9) Sample standard deviation (3.10) z score (3.11) Coefficient of variation (3.12) Coefficient of skewness ds S