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Probability Density Functions 2 Notes Spring

# Probability Density Functions 2 Notes Spring - 10 of 15 1.3...

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Unformatted text preview: 10 of 15 1.3 Normal distribution-20-10 10 20 0.0 0.2 0.4 f norm ( x , μ = , σ = 1 29 x f norm ( x 29-20-10 10 20 0.0 0.2 0.4 f norm ( x , μ = 5 , σ = 2 29 x f norm ( x 29-20-10 10 20 0.0 0.2 0.4 f norm ( x , μ =-5 , σ = 5 29 x f norm ( x 29-20-10 10 20 0.0 0.2 0.4 f norm ( x , μ = 15 , σ = 0.75 29 x f norm ( x 29 Area under curve is always 1. STANDARD NORMAL DISTRIBUTION Standard normal distribution f ( z ) . Definition 1.5 A normal distribution with μ = 0 and σ = 1. If you convert normally distributed x data into z-scores, you will have a standard normal dis- tribution. Since there are an infinite set of normal distributions, historically we con- verted x to z and then only had one standard normal distribution and one standard normal cumulative distribution F ( z ). A single table of F ( z ) could then be used to solve most probability questions involving normal distributions. With computers, we can directly use any specific normal cumulative distri- Anthony Tanbakuchi MAT167 Probability density functions 11 of 15 bution F ( x ) and very accurately find probabilities.-6-4-2 2 4 6 0.0 0.1 0.2 0.3 0.4 0.5 Standard normal distribution z f std ( z 29 FINDING PROBABILITIES INVOLVING THE NORMAL DISTRIBUTION Normal CDF: pnorm(x, mean=0, sd=1)...
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Probability Density Functions 2 Notes Spring - 10 of 15 1.3...

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