Correlation and Regression 1. Pearson's Product Moment Correlation Coefficient " [ xy - Ex Ex 2. Spearman's Rank correlation coefficient, r, = 1 - - n(n' - 1) 3. The least- squares regression line of Y against X, Y = a + bX i. b_ _xy-ExZy [xy _ 2xLy or b= - n n ii. a =y-bx or n Probability Distribution 1 . Uniform P(X = x) = _, for x = X1,X2 ,..., Xk Mean, u k +1 2 Variance, o? = K2 - 1 12 2. Binomial P(X = x)="Cop*q0-*, for x =0,1,2,.., n Mean, H = E(X) = np Variance,o' = V(X) =npq 3. Poisson P(X = x) =e*)x for x = 0,12,... x! Mean, u = E(X) = > Variance, a' = V(X) = >FORMULA LIST Sample Measurements 1. Mean, X = or fx n n 2. Median, X = Lm + 2 . C 3. Mode, * = Lma . C 4. Standard Deviation, S = Vn-1 E ( x - x) or 1 n = Vn -1 If(x - x)? or 1 in- 1 Efx _ ( [fx ) n 5. Coefficient of Variation, CV = 2 x 100 6. Mean - Mode 3 (Mean - Median) Pearson's Measure of Skewness = or Standard Deviation Standard Deviation where 1I total frequency Lm lower class boundary of a median class L mo lower class boundary of a modal class cumulative frequencies for the classes before the median class fm frequency of median class = (frequency of modal class) - (previous frequency of modal class) A 2 = (frequency of modal class) - (next frequency of modal class) class sizeQUESTION 3 a) The probability distribution of a random variable Y can be expressed as follows: P(Y = y) = =(v -1), y=2,3,4,5 0, elsewhere i) Show that the value of c = 10. (2 marks) i) Find P(Y