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,

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Presentation transcript:

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)

Sooooo……

Probability Mass Function

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: mlhttp://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?