参考案例详解lesson discrete random variables.pdfVIP

Overview This chapter will deal with the construction of probability distributions by combining the methods of descriptive statistics and probability presented in Chapter 9 and 11. Probability Distributions will describe what will probably happen instead of what actually did happen. Suppose we roll an ordinary 6-sided die sixty times and record the number of ones, twos, etc. We might get Number on die 1 2 3 4 5 6 Frequency 12 9 11 10 7 11 If I asked you what you might expect to happen if we went on rolling the die you might say that you would expect roughly the sa mber of ones, twos, etc. In saying this, you would be using a perfectly reasonable model. Models in Statistics describe situations and are used to make predictions. We could write the model out as a table: x 1 2 3 4 5 6 P (X = x) 6 x gives the value of the number shown on the die. It is a variable which can be any value from 1 to 6 . We letX be a description of the variable, so: “X is the number shown on the face of the die” We label the 2nd row P (X = x) . If x = 1, for example, we get P(X = 1) whi eans the probability that the number shown on the die is 1. So, we have x 1 2 3 4 5 6 P(X = 1 ) 6 So, we have x 1 2 3 4 5 6 P(X = 2 )