STAT 1000 Lecture Notes - Lecture 22: Fair Coin, Sample Space, Probability Theory

• School: University of Manitoba
• Department: Statistics
• Course: STAT 1000
• Professor: Mohammad Nadimi

Document Summary

Suppose we observe the following sequence of tosses: We record the proportions of observing a head: The proportions vary quite a bit early on, but in the long-run, we are bound to see proportions very close to 0. 5 consistently. Eventually, the proportion gets close to 0. 5 and stays there. (toss a fair coin 10,000 times and you will almost surely observe between 4,900 and 5,100 heads). We say that 0. 5 is the probability of observing a head. If individual outcomes are uncertain but there is a regular distribution of outcomes in a large number of repetitions. Note the term random is not the same in statistics as it is in everyday language. we often associate . This may be due to the fact that we do not observe the phenomenon enough times to observe a long-run pattern, after which regularity would be sure to emerge.