Question

why are there so many kinds of random variable like binomial, poisson and normal? can someone tell me the differences?

Answer 1

Poisson?

Answer 2

yup!

Answer 3

binomial, poisson and normal are distributions of random variables not random variables.

Answer 4

what do you mean by distributions of random variables?

Answer 5

a "random variable" is a function. bad name because it is neither random, not a variable.

Answer 6

omg and what is a function?

Answer 7

I'm going to have a hard time explaining distributions if u don't know what a function is....

Answer 8

in the simplest probability case a function will take the "outcome" of your experiment and send it to a number. this sounds abstract but think of a simple example


roll two dice. imagine you get (3,4)
if your random variable is simply the sum of faces, it would send this to 7

Answer 9

flip a coin 4 times and say your random variable counts how many heads you have. then it would send (h t h h) to the number 3, because you go 3 heads

Answer 10

function is just a result is it?

Answer 11

The problem is that the best description of of a random variable (it's density) requires very many observations so it is often convenient to describe a random variable by a single number (ie a statistic).

Answer 12

go bet $50 on a horse race. if you win you get $150 if you lose you lose your $50
if the random variable is your winnings, then it sends (win) to 150 and (lose) to -50

Answer 13

no the result is just the result. the function sends the result to a number

Answer 14

here is a simple one. flip a coin. the outcome can be H or T
a random variable could send H to 1 and T to 0

Answer 15

ummmm hmm and what about domain and range what are they

Answer 16

if we call that random variable X, then we say
\[X(H)+1\] and
\[X(T)=0\]

Answer 17

the domain of a random variable is the sample space of your experiment. set of possible outcomes

Answer 18

range is whatever it is. for example in my simple case above, the range of X was 1 and 0

Answer 19

i am giving obviously the simplest possible example to get the concept. it get more complicated quick

Answer 20

Yes, pinning down random variables is a bit tricky...

Answer 21

all this while i was thinking random variables are just lets say in a sample, we have so many random variables like in a sample of height of ppl. we have many many different heights so those heights are rv.. am i right?

Answer 22

that is just a "random variable" the "distribution" is something different. it is itself a function, which gives the probability that a random variable takes on its values

Answer 23

not quite

Answer 24

then what is it.......

Answer 25

lets call your random variable "height"

Answer 26

your input is your set of people
your output is their heights

Answer 27

Repeating myself:

The problem is that the best description of of a random variable (it's density) requires very many observations so it is often convenient to describe a random variable by a single number (ie a statistic).

Answer 28

so it sends
Joe to 5'9''
Tom to 6'2''
Mary to 5'6''
etc

Answer 29

@estudier this may be a statistic version of it i am not familair

Answer 30

oh! rv is the height!

Answer 31

in your example yes

Answer 32

in my simple example the input of the random variable is H or T and the output is 1 or 0

Answer 33

lets imagine you play the lottery. do you?

Answer 34

why is there numbers??? i thought a coin just has out put head or tail?
input also head or tail..

Answer 35

nup! am a student

Answer 36

but i know lottery!

Answer 37

yes the coin comes up heads or tails. but i made up a random variable that says "if you get H, put 1 and if you get T put 0"

Answer 38

then if i flip a coin ten times and add these up it tells me how many heads i get

Answer 39

uh huh

Answer 40

back to the lotter. you buy a ticket for $1
if you win you win $500 and of you don't you lose your $1
right?

Answer 41

u lose ur one dollar! if you lose

Answer 42

yup yup!

Answer 43

so i can say
let X be the amount you win. then X takes on two values. X could be 500 (i win) or X could be -1( you lose)

Answer 44

in math we can write this as X(win) = 500. X(lose) = -1

Answer 45

uh huh!

Answer 46

now lets say the probability i win is .002 and the probability i lose is therefore .998

Answer 47

so now i know the probability that X takes on its two values those probabilities are .002 and .998

Answer 48

yup

Answer 49

so i can say
\[P(X=500)=.002\] and
\[P(X=-1)=.998\]

Answer 50

OMG COOL!

Answer 51

now these alphabets make some sense now..

Answer 52

in english, the probability that X is 500 (meaning i win) is .002 and the probability that X is -1 (meaning i lose) is .998

Answer 53

yup yup yup!!

Answer 54

so i have my random variable, it is X
i know the probability it takes on each of its two values.
together they give the
DISTRIBUTION OF THE RANDOM VARIABLE

Answer 55

now this was a very very simple example. you can imagine it gets deep quick. but at least we have the idea right? a random variable is a function that assigns a number to the outcome of an experiment

Answer 56

oooooooooooookkkkkkkkkkkkkkkkkkkkkk..............
so whats with the poisson and and.... who is that binomial....normaal........

Answer 57

yup! got it more or less

Answer 58

and the "distribution" of the random variable is a description of the probability that it takes on each of its values

Answer 59

now i don't have a quick snap answer to these, especially not poisson but i can give you an idea. start with binomial. lets say you flip a coin 4 times. not a fair coin, a coin where the probability you get heads is .2 and the probability you get tails is .8

Answer 60

let X be the random variable that counts the number of heads. so for example X sends the outcome (h t t t) to the number 1 cause you got one head

Answer 61

the possible values of X are 0, 1, 2, 3 and 4 since those are the number of heads you can get.

Answer 62

\[P(X=0)=(.8)^4\] because it means you got 4 tails in a row

Answer 63

can we discuss this on msn it's so lagging here

Answer 64

\[P(X=1)=4\times .2\times (.8)^3\] because you got 1 head, 3 tails and there are four ways to do this.

finish out this scheme for
\[P(X)=2,P(X)=3,P(X)=4\] and you will have a binomial distribution. if that is not clear, and my guess is it isn't, you need to understand the basics (am a not judging, just suggesting) before you will understand what a distribution of a random variable is

Answer 65

i've through my notes a few times already am just almost memorizing though i do understand but idea isn't very there..

Answer 66

read

Answer 67

The outcome of a die roll is not predictable although u know that it will be in 1 to 6 (range). The outcome is a random variable.

The function that specifies the probability that k will be a value in the range is

p_k = 1/6 (and the sum of all the p_k's in the range is 1).

An experiment that measures p_k directly will provide an estimation.

p_k = n_k/N which is just the relative frequency of k in N throws.

n_k/N is a random number.

U can describe this scenario with a distribution and if u take a set of random numbers from the distribution it will in principle reflect the probabilities described.

Answer 68

hi im quite lost in the sea of words