product moment corre- lation coefficient (r) is given by Equation 1.19 or 1.20. A special case of this probability law is when events are mutually exclusive, i.e. the occurrence of one event prevents the other from (1.19) happening. Then Equation 1.25 is obtained. noxoy P(AorB)=P(A)+P(B) (1.25) ( x x x (y y y) (1.20) If A and B are two events then the probability that they may occur together is given by Equation 1.26 or 1.27. = P(A) x P(BA) (1.26) The value of r varies from +1, when all the points lie on a straight P and = P(B) x P(A ) (1.27) line and the number of defects increase with time to-1, when all the points lie on a straight line but defects decreases with time. When r P(B|A) is the probability that event B will occur assuming that = 0 the points are widely scattered and there is said to be no event A has already occurred and P(A|B) is the probability that event correlation between the X and y values. A will occur assuming that event B has already occurred. A special The standard error of estimation in r is given by Equation 1.21. case of this probability law is when A and B are independent events, i.e. the occurrence of one event has no influence on the probability (1.21) of the other event occurring. Then Equation 1.28 is obtained. P andB)=P(A)xP(B (1.28) In about 95% of cases, the actual values will lie within plus or minus twice the standard error of estimated values given by the Bayes' theorem on probability may be stated as in Equation 1.29. regression equation. This is shown by lines CD and EF in Figure 1.6. Almost all the values will be within plus or minus three times the (1.29) standard error of estimated values. It should be noted that o is the variability of the y values, whereas As an example of the use of Bayes' theorem suppose that a S is a measure of the variability of the y values as they differ from the regression which exists between X and y. If there is no regression company discovers that 80% of those who bought its multiplexers in a year had been on the company's training course. 3