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Statistics for Engineers
October 31, 2007
Outline - The Normal Distribution and the Central Limit
Theorem
1. The normal distribution.
2. The standard normal distribution.
3. Any normal distribution from standard normal distribution.
4. i.i.d. random variables X1 , . . . , Xn
5. The sum Y of i.i.d. random variables
6. The sum of independent normals is normal
7. The Central Limit Theorem
8. The distribution of the sample mean
Homework
1. Read Section 3.5.
2. Do problems 3.26, 3.27 of the text.
Useful R
> pnorm(1,0,1)
[1] 0.8413447
> dnorm(0,0,1)
[1] 0.3989423
> rnorm(10,0,1)
[1] 0.3046967 -0.4709662 -0.9043858 -1.0532504
[7] 0.9262808 0.2212721 -0.2212027 1.0105646
> qnorm(.75,0,1)
[1] 0.6744898
>
0.7853981
0.9422723
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