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Unformatted text preview: Stet 400 teture I Review (2.6) o Poisson Processes, Poisson distribution. o Mean, variance and m.g.f. of Poisson distribution. o Poisson Approximation to Binomial distribution. Today's Lecture (3.3) o Continuous random variable and its c.d.f. o Probability density function (p.d.f.), its properties. r Mean, variance, moment generating function o Percentiles for p.d.f. o Comparison between discrete and continuous random variables Stat ,100 Leturc I SDrins 2012 Continuous-type random variable and its c.d.f. The random variable X is a continuous random variable if X takes all values in an interval of numbers. r Wheel of fortune: the angle of the pointer is within [0,,360o). o The length of time it takes to check out at Walmart in the weekend. r The time we wait to see the next volcano eruption in the wodd. Note: o When X is continuous, P(X - r) : 0 for all s. The probability mass function is meaningless. o Although we cannot assign a probability to any value of X, we are able to assign probabilities to intervals: e.g. P(X - 1) : 0, but P(0.999 < X < 1.001) can be > 0. 2oI12 Stat 4m tahrre I Spring 2012 Probability density function Definition: The probability density function (p.d.f.) of a continuous random variable X is f"(z) : Iim ,+0 Fy(r+t)-Fa(r) = Fk@) t Example 1 La X he r curiuuous mudmr uriable p.irh thc erlmdath: disuitnLtim 6mtio t<0, 0 5r 5.1, rt.tt = r-4. r>1....
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