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Math 4030 4b Continuous Random Variables

- Density Function
- PDF and CDF
- Mean and Variance
- Normal Distribution

Difficulties

- Probability at a value
- Addition rule
- 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

Properties of f(x) and F(x)

Mean and Variance

Normal N(?, ?2) (Sec. 5.2)

Standard Normal N(0, 1)

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

From General Normal to Standard Normal

- If X N(µ, ?2), then the transformation
- Z (X - µ) / ? results Z N(0, 1).

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

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