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## Math 4030

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### Title: Math 4030 3a Continuous Random Variables Author: Wendy Last modified by: Wendy Created Date: 2/6/2004 6:15:45 PM Document presentation format – PowerPoint PPT presentation

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Title: Math 4030

1
Math 4030 4b Continuous Random Variables
• Density Function
• PDF and CDF
• Mean and Variance
• Normal Distribution

2
Difficulties
• Probability at a value
• Axiom of probability
• Zero probability event vs. empty event

Approach (Sec. 5.1)
• Probability density function (pdf) f(x)
• Area for probability ? cumulative distribution
function (cdf) F(x)
• Integral for area, fundamental theorem of
calculus

3
Properties of f(x) and F(x)
Mean and Variance
4
Normal N(?, ?2) (Sec. 5.2)
Standard Normal N(0, 1)
5
z? notation A z-value that the probability for Z
to be greater than this value is exactly ?. Or
the cut point of the standard normal curve that
makes the area of the right tail exactly ?.
68-95-99.7 Rule
6
From General Normal to Standard Normal
• If X N(µ, ?2), then the transformation
• Z (X - µ) / ? results Z N(0, 1).

7
Normal Approximation to Binomial (Sec. 5.3)
Or if X has binomial distribution with parameters
n and p, then
• For large n, npgt15, and n(1-p)gt15.
• Correction for continuity