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Note:
The variables listed above cannot be archived.
Distribution Functions
DISTR menu
To display the DISTR menu, press y =.
DISTR DRAW
1: normalpdf(
2: normalcdf(
3: invNorm(
4: invT(
5: tpdf(
6: tcdf(
7: c
2 pdf(
8: c
2 cdf
9:
Üpdf(
0:
Ücdf(
A: binompdf(
B: binomcdf(
C: poissonpdf(
D: poissoncdf(
E: geometpdf(
F: geometcdf(
nn probability density function
nn cumulative distribution function
Inverse cumulative normal distribution
Inverse cumulative Student-t distribution
Student-t probability density
Student-t distribution probability
Chi-square probability density
Chi-square distribution probability wÜ probability density wÜ distribution probability
Binomial probability
Binomial cumulative density
Poisson probability
Poisson cumulative density
Geometric probability
Geometric cumulative density
Note:
L1â99 and 1â99 specify infinity. If you want to view the area left of
upperbound
, for example, specify
lowerbound
=
L1â99.
normalpdf( normalpdf(
computes the probability density function (
) for the normal distribution at a specified
x
value. The defaults are mean m=0 and standard deviation s=1. To plot the normal distribution, paste
normalpdf(
to the Y= editor. The probability density function (pdf) is:
=
2
–
–
x
–
2
2
2
,
0
Chapter 13: Inferential Statistics and Distributions 235
normalpdf(x
[
,
m
,
s]
)
Note: For this example,
Xmin = 28
Xmax = 42
Xscl = 1
Ymin = 0
Ymax = .2
Yscl = .1
Note:
For plotting the normal distribution, you can set window variables
Xmin
and
Xmax
so that the mean m falls between them, and then select
0:ZoomFit
from the
ZOOM
menu.
normalcdf( normalcdf(
computes the normal distribution probability between
lowerbound
and
upperbound
for the specified mean m and standard deviation s. The defaults are m=0 and s=1.
normalcdf(lowerbound,upperbound[, m
,
s
])
invNorm( invNorm(
computes the inverse cumulative normal distribution function for a given
area
under the normal distribution curve specified by mean m and standard deviation s. It calculates the
x
value associated with an
area
to the left of the
x
value. 0
area
1 must be true. The defaults are m=0 and s=1.
invNorm(area[, m
,
s
])
invT( invT(
computes the inverse cumulative Student-t probability function specified by Degree of
Freedom, df for a given Area under the curve.
Chapter 13: Inferential Statistics and Distributions 236
invT(area,df)
tpdf( tpdf(
computes the probability density function (
) for the Student-
t
distribution at a specified
x
value.
df
(degrees of freedom) must be > 0. To plot the Student-
t
distribution, paste
tpdf(
to the Y= editor. The probability density function (
) is:
=
/2
1 +
x
2
–
df
+ 1
/2
df
tpdf(x,df)
Note: For this example,
Xmin =
L
4.5
Xmax = 4.5
Ymin = 0
Ymax = .4
tcdf( tcdf(
computes the Student-
t
distribution probability between
lowerbound
and
upperbound
for the specified
df
(degrees of freedom), which must be > 0.
tcdf(lowerbound,upperbound,df) c
2
pdf(
c
2
pdf(
computes the probability density function (
) for the c
2
(chi-square) distribution at a specified
x
value.
df
(degrees of freedom) must be an integer > 0. To plot the c
2
distribution, paste c
2
pdf(
to the Y= editor. The probability density function (
) is:
Chapter 13: Inferential Statistics and Distributions 237
= c
2
pdf(x,df)
df/2
x
– 1
e
– x/2
,
x
0
Note: For this example,
Xmin = 0
Xmax = 30
Ymin =
L
.02
Ymax = .132
c
2
cdf(
c
2
cdf(
computes the c
2
(chi-square) distribution probability between
lowerbound
and
upperbound
for the specified
df
(degrees of freedom), which must be an integer > 0.
c
2
cdf(lowerbound,upperbound,df)
Fpdf(
Ü
pdf(
computes the probability density function (
numerator df
) for the
Ü distribution at a specified paste
Ü
pdf(
to the Y= editor. The probability density function (
) is:
x
value.
(degrees of freedom) and
denominator df
must be integers > 0. To plot the
Ü distribution,
=
n/2
d
n/2
x
n/2 – 1
1 + nx/d
–
n
+
d
/2
,
x
0 where
n
= numerator degrees of freedom
d
= denominator degrees of freedom
Chapter 13: Inferential Statistics and Distributions 238
Ü
pdf(x,numerator df,denominator df)
Note: For this example,
Xmin = 0
Xmax = 5
Ymin = 0
Ymax = 1
Fcdf(
Ü
cdf(
computes the
Ü distribution probability between
lowerbound
and
upperbound
for the specified
numerator df
(degrees of freedom) and
denominator df
.
numerator df
and
denominator df
must be integers
> 0.
Ü
cdf(lowerbound,upperbound,numerator df,denominator df)
binompdf binompdf(
computes a probability at
x
for the discrete binomial distribution with the specified
numtrials
and probability of success (
p
) on each trial.
x
can be an integer or a list of integers. 0
p
1 must be true.
numtrials
must be an integer > 0. If you do not specify
x
, a list of probabilities from 0 to
numtrials
is returned. The probability density function (
) is:
=
x p x
1 –
p
n
–
x
,
x
= 0,1,...,n where
n = numtrials
binompdf(numtrials,p[,x])
binomcdf( binomcdf(
computes a cumulative probability at
x
for the discrete binomial distribution with the specified
numtrials
and probability of success (
p
) on each trial.
x
can be a real number or a list of real numbers. 0
p
1 must be true.
numtrials
must be an integer > 0. If you do not specify
x
, a list of cumulative probabilities is returned.
Chapter 13: Inferential Statistics and Distributions 239
binomcdf(numtrials,p[,x])
poissonpdf( poissonpdf(
computes a probability at
x
for the discrete Poisson distribution with the specified mean m, which must be a real number > 0.
x
can be an integer or a list of integers. The probability density function (
) is:
f x
=
e
–
x
x!
,
x
= 0,1,2,...
poissonpdf(
m
,x)
poissoncdf( poissoncdf(
computes a cumulative probability at
x
for the discrete Poisson distribution with the specified mean m, which must be a real number > 0.
x
can be a real number or a list of real numbers.
poissoncdf(
m
,x)
geometpdf( geometpdf(
computes a probability at
x
, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success
p
. 0
p
1 must be true.
x
can be an integer or a list of integers. The probability density function (pdf) is:
f x
=
–
p
x
– 1
,
x
= 1,2,...
geometpdf(p,x)
Chapter 13: Inferential Statistics and Distributions 240
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