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Biostatistics Lecture 5

# Then the probability you will make shots and you will

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Unformatted text preview: shots. Then the probability you will make shots (and you will miss shots) is See the box on Book Page 110. ) ( ) . Let’s look at the probabilities (which add up to 1) of making none to all ten to each case in between. Made shots Probability of this case occurring (out of 10) 0 ( )( ) 1 ( )( ) 2 ( )( ) 3 ( )( ) 4 ( )( ) 5 ( )( ) 6 ( )( ) 7 ( )( ) 8 ( )( ) 9 ( )( ) )( ) 10 ( A binomial random variable. See note on BInS on page 110. A few notes: Random and variable mean the same thing as in the past. Binary means two possible outcomes. Independent: What happens in one trial does not affect what happens in any of the others (in the free throw example, whether you made or missed the previous free throw, there is still a 70% chance you will make the next one). See Book Examples 3.6.4 – 3.6.7. Back to the free throw example to introduce mean, variance and standard deviation for a binomial random variable. 70% free throw shooter, shoot 3 shots. The probability distribution (the possible outcomes and their respective probabilities): Made shots Probability of this case occuring (out of 3) 0 ( )( ) 1 )( ) 2 ( )( ) 3 Where ( ( )( ) is the number of shots made, then the expected value of is and the variance is and thus the standard deviation is In general, for binomial random variable In this example we see that , the mean is and the variance is ( ). The standard deviation might not seem to have much meaning right now, but it will be useful to us later. Section 3.7 Fitting a Binomial Distribution to Data See Book Example 3.7.1....
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