Chap5-slide

Chapter 5 Properties of Random Variables Xuerong Meggie Wen Missouri University of Science and Technology Chapter 5 Properties of Random Variables - p. 1/139

Random Samples Definition 1. If X 1 , . . . , X n are independently identically distributed (iid), then ( X 1 , . . . , X n ) is called a simple random sample. Chapter 5 Properties of Random Variables - p. 2/139

joint pdf Remarks: 1. If X 1 , . . . , X n is a random sample of size n with marginal pdf f ( x i ) , then the joint pdf is: f ( x 1 , . . . , x n ) = f ( x 1 ) f ( x 2 ) . . . f ( x n ) = Π n i =1 f ( x i ) . 2. If the common marginal pdf denpends on a parameter θ , then the joint pdf is: f ( x 1 , . . . , x n | θ ) = Π n i =1 f ( x i | θ ) . Chapter 5 Properties of Random Variables - p. 3/139