Hp 50g Graphing Calculator Uživatelský manuál stáhnout pdf (Strana 554)

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101

Page 17-5

Poisson distribution

The probability mass function of the Poisson distribution is given by

In this expression, if the random variable X represents the number of

occurrences of an event or observation per unit time, length, area, volume, etc.,

then the parameter l represents the average number of occurrences per unit

time, length, area, volume, etc. The cumulative distribution function for the

Poisson distribution is given by

Next, use function DEFINE („à) to define the following probability mass

functions (pmf) and cumulative distribution functions (cdf):

DEFINE(pmfb(n,p,x) = COMB(n,x)*p^x*(1-p)^(n-x))

DEFINE(cdfb(n,p,x) =

Σ(k=0,x,pmfb(n,p,k)))

DEFINE(pmfp(

λ,x) = EXP(-λ)*λ^x/x!)

DEFINE(cdfp(

λ,x) = Σ(k=0,x,pmfp(λ,x)))

The function names stand for:

Θ pmfb: probability mass function for the binomial distribution

Θ cdfb: cumulative distribution function for the binomial distribution

Θ pmfp: probability mass function for the Poisson distribution

Θ cdfp: cumulative distribution function for the Poisson distribution

Examples of calculations using these functions are shown next:

nxxpnfxpnF

,...,2,1,0,),,(),,(

∑

∞=

⋅

−

,...,2,1,0,

),( x

∞==

∑

,...,2,1,0,),(),(

xxfxF

λλ

1 2 ... 549 550 551 552 553 554 555 556 557 558 559 ... 886 887

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