| Term Papers Count: 63,000 | ||
| Home | Join | Login | Logout | Forgot Password | FAQ | Contact | ||
|
| ||
Term Papers on Formulas
Formulas FORMULAS / STRATEGY FOR STATISTICS Probability Complement Law - P(A’) = 1 - P(A) Laws Of Addition - P(A È B) = P(A) + P(B) - P(A Ç B), if A and B not mutually exclusive P(A È B) = P(A) + P(B), if A and B are mutually exclusive Conditional Probability - P(A|B) = P(A Ç B) P(B) Independent Condition - If A and B are independent, P(A Ç B) = P(A) x P(B) Laws Of Multiplication - If A and B are dependent, P(A Ç B) = P(A) x P(B|A) or P(A Ç B) = P(B) x P(A|B) Descriptive Statistics Population Mean, m= å all values N Sample Mean, x’ = å all values n Population Variance, s2 = å (X - m)2 N Sample Variance, S2 = å (x - x’)2 n-1 Standard Deviation = square root of s2 or S2 Probability Distribution Expected Value, E(x) = å all x P(xi = x) = m Properties of E(x), E(a) = a E(ax) = aE(x) E(ax ± b) = aE(x) ± b E(x1 ± x2) = E(x1) ± E(x2) E(x2) = å all x2 P(xi = x) Variance, Var(x) = E(x - m)2 or Var(x) = E(x2) - n(x’)2 Properties of Var(x), Var(a) = 0 Var(ax) = a2Var(x) Var(ax ± b) = a2E(x) Var(x1 ± x2) = Var(x1) + Var(x2) E(x2) = å all x2 P(xi = x) Standard Deviation = square root of var(x) Binomial Distribution - x ~ Bin (n , p) Characteristics, Experiment consist of a number of trials Results of trials are only either success or failure Probability of each test between trials are the same E(x) = np Var(x) = npq Continuous Distribution - x ~ N(m , s2) Standardising, z = x - m s Normal Approximation to Binomial Distribution - x ~ N(np , npq) Conditions, Number of trials n > 50 Must use continuity correction Joint Probability Conditional Mean - E(x | y=y1) = å all x P(xi | y) E(XY) = å [all x all y P(xi = x and yi = y)] When x and y are independent, E(XY) = E(X) E(Y) Covariance of 2 random variables, sxy - Cov(XY) = E(XY) - E(X)E(Y) When X and Y are independent, Cov(XY) = 0, since E(XY) = E(X)E(Y) Correlation Coefficient, r = Cov(XY) ,-1 £ r £ 1 Ö[Var(x) Var(y)] Formula for Variance of linear combinations of 2 dependent variables - Var(X ± Y) = Var(X) + Var (Y) ± 2Cov(XY) Var(aX ± bY) = a2Var(X) + b2Var (Y) ± 2abCov(XY) Distribution Of Sample Mean Sample Proportion Let X denote the population variable. m the population mean and s2 the population variance. then, x’ ~ N(m,s2/n) Let P denote the population proportion with proportion P with n, the number of samples, then P ~ N { p , p [(1-p)/n] } if P is unknown, P ~ N { P , P [(1-P)/n] } approx. where P is the sample proportion with the use of continuity correction x ± (1/2n) Theory Of Estimation Mean Square Error - MSE = E(V - q)2 where V is the value of the estimator from the true value q Best estimator of the true value is the one that yields the lowest MSE Confidence Interval - The interval of which the true value is probable to be included. 3 Cases Of Formula For Confidence Interval - For population mean where m, s2 given, - m = x’ ± (s2/n)1/2 Zsig level m given but s2 unknown, samples size n > 50 - m = x’ ± (S2/n)1/2 Zsig level m given but s2 unknown, samples size n 50 - mD = (x’ ± y’) ± (Sx2/nx + Sy2/ny)1/2 Zsig level m given but s2 unknown, samples size n < 50 - mD = (x’ ± y’) ± (Sp2/nx + Sp2/ny)1/2 tsig level where pooled variance, Sp2 = S(x... This is ONLY a preview of the article. If you would like to view the entire document, you must subscribe to Digital Term Papers. Please register below now! Digital Term Papers has over 63,000 essays, term papers, and book notes online. Many paper sites will charge you hundreds of dollars for a single paper. Digital Term Papers only charges $14.95 for a one month membership with instant account activation! Don't waste anymore time! Join NOW!!!
|
|
Copyright 1998-2007 Digital Term Papers. All Rights Reserved.
Forgot Password
Cancel Account
Privacy Policy
Disclaimer
Contact Us
Essay List: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 |