# stat400lec13 - Statistics 400 Lecture 13(Sep 23 Continuous...

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Statistics 400 Lecture 13 (Sep 23) Continuous Distributions Random Variable: (R.V.) is a variable whose value is a numerical outcome of a random phenomenon. Notation : X, Y, Z Note : When a random variable X describes a random phenomenon, the sample space S just lists the possible values the random variable takes. Discrete Random Variables: A discrete R.V. has a countable number of possible outcomes These outcomes have a individual probabilities attached to them Probability Distributions: Lists the values of X Lists their respective probabilities Value of X x 1 x 2 x 3 x 4 x 5 x k Probability mass function : f(x) f(x 1 ) f(x 2 ) f(x 3 ) f(x 4 ) f(x 5 ) f(x k ) Properties of p.m.f f(x) : (a) f(x)>0; ( b ) = 1 ) ( x f ; ( c ) P(X=x)=f(x). Ping Ma Lecture 13 Fall 2005 - 1 -

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Continuous Random Variables: Takes on all values in an interval of numbers The probability distribution of X is described by a probability density function (p.d.f). The probability of an event is the area under the p.d.f. and over the
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stat400lec13 - Statistics 400 Lecture 13(Sep 23 Continuous...

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