Transcript Probability
Probability Statistics 2126 Introduction • This stuff can be a bit hard, but don’t be afraid • We use probability for our purposes, so it will be a tool, not an end in and of itself • Why does this stuff matter to statistics • Because we want to know about populations, but we only have samples example • Say you flip a coin 10 times • Say you get 10 heads, probably not a fair coin • Now it could happen, it could be fair • But it is so unlikely we would probably conclude that it is a fixed coin • The only way to really know would be to flip it an infinite number of times A decision • About 8 / 10 heads is roughly a 5 percent probability of it being fair • This is where we usually draw the line • It also tends to fit with our intuitive feel What is probability • The total number of desired outcomes divided by the total number of possible outcomes • It is just that simple • So what is the probability of getting a red card • What is the probability of rolling a 4 on a 6 sided die? A bit more complicated… • • • • • • • 2 dice What is the probability of rolling a 7? Well how many ways can you get a 7? 1,6 2,5 3,4 4,3 5,2 6,1 36 possible rolls 6/36 = 1/6 or .167 What about NOT rolling a 7? properties • 0 <= p <= 1 • A probability of 1 is all outcomes • 0 is something that never happens Spin (x) Frequency (f) 1 2 2 5 3 3 4 9 5 1 Sooooo…… 0.5 0.4 0.3 0.2 0.1 0 1 2 3 4 5 Probability Mass Function 0.5 0.4 0.3 0.2 0.1 0 1 2 3 4 5 However • Most of the distributions that we look at don’t have some shape that we can easily find the area of • Like say, a normal distribution • How would we find the area under that? • Well calculus • Or a z table…. Well this must all have a point • Using a z table • Or this VERY cool website: • http://davidmlane.com/hyperstat/z_table.ht ml • So if you know the z, you can find out what the probability of getting a z score at a certain level is. So what is the probability of having an IQ greater than 107? x z 107 100 z 15 z 7 / 15 z .47 p ( z .47) .3192