HP 48gII Graphing Calculator Manual do Utilizador descarregar pdf (Página 559)

100

101

Page 17-6

Examples of calculations using these functions are shown next:

Continuous probability distributions

The probability distribution for a continuous random variable, X, is

characterized by a function f(x) known as the probability density function (pdf).

The pdf has the following properties: f(x) > 0, for all x, and

.1)( =

∫

∞+

∞−

dxxf

Probabilities are calculated using the cumulative distribution function (cdf), F(x),

defined by

∫

∞−

==<

dfxFxXP ξξ )()(][ , where P[X<x] stands for “the

probability that the random variable X is less than the value x”.

In this section we describe several continuous probability distributions

including the gamma, exponential, beta, and Weibull distributions. These

distributions are described in any statistics textbook. Some of these

distributions make use of a the Gamma function

defined earlier, which is

calculated in the calculator by using the factorial function as Γ(x) = (x-1)!, for

any real number x.

The gamma distribution

The probability distribution function (pdf) for the gamma distribution is given

;0,0,0),exp(

)(

>>>−⋅⋅

−

βα

αβ

xfor

xxf

PX x Fx f d

[]() ().

<= =

−∞

∫

ξξ

1 2 ... 554 555 556 557 558 559 560 561 562 563 564 ... 863 864

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