- StudyBlue
- Illinois
- University of Illinois - Urbana-Champaign
- Natural Resources And Environmental Science
- Natural Resources And Environmental Science 421
- Yannarell
- Random Continuous Variables

Katie D.

I=[a, b]

interval

uniform random variable

over defined interval I, URV has equal probability of taking on the value in any evenly spaced sub-interval, U, and 0 probability outside

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probability density function

f(x)=1/(b-a) for a <=x<=b

probability of occurring in any subinterval [i, j] is equal to area under PDF from interval [i,j]

specific value (y-value) of the function for every value of x for which the function is defined

cumulative density function

f(y)=P(x<y) y varies from a to b

area under PDF for all values of x<y

probability of observing a value <x

used to calculate tail probability

tail probability

CDF includes probability of all values y<x

random normal variable

bell curve distribution

most values of the variable cluster around a central value, probability of obtaining other values below

mean

central value

standard deviation

measure of spread of data

shift operation

addition

scale operation

multiplication

Z transformation

z= (yi-ý)/σ (sum of squares)/SD

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standard normal distribution

normal distribution with mean=1 and std deviation=1

log-normal random variable

if ln(x)~N(mew, sigma) then x is log-normal

e.g. body mass of organisms

PDF, E(x), Var

exponential random variable

related to Poisson random variables, "spaces" between Poisson events

PDF, E(x), Var

probability density function equation

f(x)=1/(b-a) for a<=x<= b

0 otherwise

area under PDF

1/(b-a)*(b-a)

height of PDF*width

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