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Normal Distribution

Normal Distribution - Stat 48 Lecture May 9th Normal...

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Stat 48 Lecture May 9 th Normal Distribution Dr Linda Penas Spring 2007 1 Continuous Distributions (p. 106) DEFN : A random variable is said to be continuous if its values can be put into a 1-1 correspondence to the real numbers. (i.e., measured on a continuous scale) Continuous Prob. Distributions DEFN : probability density function (pdf): for a continuous random variable X is a curve such that the area under the curve between two points a and b is equal to the probability that the random variable X falls between a and b. Continuous Prob. Distributions Cumulative Distribution Function (cdf ) of a continuous random variable X is given by ( ) ( ) ( ) x F x P X x f t dt −∞ = = P(a < X < b) = area under the curve between a and b = F(b) - F(a) a b P(a < X < b) pdf must be nonnegative and the entire area under the curve is 1. For continuous random variables only, ( ) ( ) = ( ) ( ) P a X b P a X b P a X b P a X b = < < = < < Q: Why does that work for continuous rvs? A: Because the area of a single point = 0 P(X = a) = 0 ( ) ( ) 0 a a P a X a f x dx = =
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