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LEC14 Continuous Dist

LEC14 Continuous Dist - Continuous Random Variables r.v X =...

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Continuous Random Variables r.v. X = lifetime of a battery number of observations = 50 number of categories in histogram = 9 interval size 1.0 .3 .2 .1 lifetime in 100-hrs Freq Function f(x)=.5e -.5x fits the histogram, sort of. From histogram, add blocks to get P(1<X<2)=.2
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To study the lifetime more closely, collect more data number of observations = 500 number of categories in histogram = 36 interval size 0.25 .3 .2 .1 lifetime in 100-hrs Freq Function f(x)=.5e -.5x fits the histogram From histogram, add blocks to get P(1<X<2)=.2 2
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To study the lifetime even more closely, collect more data number of observations number of categories in histogram interval size 0 Lifetime 100 hrs freq 0.1 0.2 0.3 Function f(x)=.5e -.5x fits the histogram From exponential function P(1<X<2)= . . . 5 27 5 1 2 e dx x - = 3
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Definition of Probability Distribution for a Continuous Random Variable Let X be a continuous random variable. The probability distribution of X is a function f(x) such that for any two numbers a and b with a
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