Thread: sampling without replacement

say i have fifty objects and 1 is the object of interest.With replacement i can modell this as a geometric distribution to find the expectation of the number of bernouli trials required until i pick the object of interest.But if there is no replacemnt then the probabilities change so how do i model this scenario in order to find quantities such as expoectation and variance?

Please be more specific. Are you drawing a sample of fixed size (5 objects, say), or do you have something else in mind like drawing objects until you draw your special object?

i have n marbles. All are white except for one which is blue.If i continually choose one marble at a time without replacement, what is the expectation until i choose the blue?

I think i have figured it out, because my notes have something on this type of distribution, so i have solved the question, but i still don't fully understand the logic, which is annoying.

Originally Posted by ulysses123

i have n marbles. All are white except for one which is blue.If i continually choose one marble at a time without replacement, what is the expectation until i choose the blue?

I think i have figured it out, because my notes have something on this type of distribution, so i have solved the question, but i still don't fully understand the logic, which is annoying.

Let X be the random variable of the number of white marbles chosen before a blue marble is chosen.

Draw a tree diagram to an extend where it's sufficient for you to see a pattern.

P(X=0)=1/n

P(X=1)=((n-1)/n) x 1/(n-1) =1/n

P(X=2)= ((n-1)/n) x ((n-2)/(n-1)) x (1/(n-2)) = 1/n

...

P(X=n-1)=1/n

E(X)=0+1/n+2/n+3/n+...+(n-1)/n

and the sum of this AP is (n-1)/2

so if you have 50 marbles, you are expected to pick (50-1)/2 white marbles before the blue marble is picked.