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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.

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Probability

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  1. Probability Statistics 2126

  2. 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

  3. 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

  4. 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

  5. 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?

  6. 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?

  7. properties • 0 <= p <= 1 • A probability of 1 is all outcomes • 0 is something that never happens

  8. Sooooo……

  9. Probability Mass Function

  10. 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….

  11. Well this must all have a point • Using a z table • Or this VERY cool website: • http://davidmlane.com/hyperstat/z_table.html • So if you know the z, you can find out what the probability of getting a z score at a certain level is.

  12. So what is the probability of having an IQ greater than 107?

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