In Problems 5–16, the survey has bias. (a) Determine the type of bias. (b) Suggest a remedy.
5. A retail store manager wants to conduct a study regarding the shopping habits of his customers. He selects the first 60 customers who enter his store on a Saturday morning.
Lecture 19 Nicole Rubenstein November 7, 2017 Introductory example Let Y and Y have the joint probability density function given by 1 2 ( e▯(y1+y2); y > 0;y > 0 f(y ;y ) = 1 2 : 1 2 0; elsewhere We know that for any y > 0 the conditional density function of Y given that Y = y is 2 1 2 2 f(y jy ) = e ▯y 1; 1 2 which is free of y 2 This implies that the probabilities associated with Y are 1he same, regardless of the observed value of Y 2 Independence De▯nition 19.1. Let Y have distribution function F (y );Y have distribution function F (y ); and Y and 1 1 1 2 2 2 1 Y2have joint distribution function F(y ;y1): 2hen Y and 1 are sa2d to be independent if and only if F(y 1y 2 = F (1 )1 (y2) 2 for every pair of real number (y ;1 )2 If Y a1d Y are2not independent, we call them dependent. We can check the introductory example: Z Z
