# Normal - Le arning Obje s ctive cognizeand...

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Learning Objectives Recognize and use the probability density function and cumulative distribution function of a normal random variable Define standard normal random variable Use standard normal table to calculate probabilities or to infer the value of the random variable from a given probability

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Why care about Normal? Convenient to work with so often used to approximate other distributions Many real interesting variables are normally distributed
Central Limit Theorem Sum of a large number of independent and identically distributed RVs is a new RV that has an approximately normal CDF

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Example Assume that in a healthy population that cerebral blood flow (CBF) is normally distributed with mean 75 and standard deviation of 17. If a patient is classified as “at risk” for stroke if CBF < 40, what proportion of healthy patients will be mistakenly classified as being at risk?
Normal RV is normal or Gaussian if PDF is X ~ N( μ , σ ) f X x (29 = 1 2 π σ e - x ( 29 2 2 2 mean ( μ ) variance ( σ 2 )

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f X x (29 = e x -10 -5 0 5 10 0 1 2 3 4 5 x
-10 -5 0 5 10 0 1 2 3 4 5 x f X x (29 = e - x

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f X x (29 = e - x 2 -10 -5 0 5 10 0 0.2 0.4 0.6 0.8 1 x
f X x (29 = e - Ax 2 0.00 0.50 1.00 1.50 2.00 -10 -5 0 5 10 x 1 2 0.5 A

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f X x (29 = Be - x 2 0.00 0.50 1.00 1.50 2.00 -10 -5 0 5 10 x 1 2 0.5 B
0.00

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Normal - Le arning Obje s ctive cognizeand...

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