Probability And Statistics

Probability and statistics are deeply connected because all statistical statements are at bot- tom statements about probability. Despite this the two sometimes feel like very different subjects. Probability is logically self-contained& there are a few rules and answers all follow logically from the rules, though computations can be tricky. In statistics we apply proba- bility to draw conclusions from data. This can be messy and usually involves as much art as science.

Probability example

You have a fair coin (equal probability of heads or tails). You will toss it 100 times. What is the probability of 60 or more heads? There is only one answer (about 0.028444) and we will learn how to compute it.

Statistics example

You have a coin of unknown provenance. To investigate whether it is fair you toss it 100 times and count the number of heads. Let s say you count 60 heads. Your job as a statis- tician is to draw a conclusion (inference) from this data. There are many ways to proceed, both in terms of the form the conclusion takes and the probability computations used to justify the conclusion.