66 views

Expected number of trials for all possible outcomes to happen

Suppose that in each trial there are exactly $n$ possible outcomes with probabilities $p_1, \dots, p_n$ which sum to $1$. I wonder what's the expected number of trials for all outcomes to happen at ...
63 views

Expected number of dice throws to fill out a table.

Say I have a table of numbers ${1,2,3,4,5,6}$. Every time I throw a fair die, if the position in the table is unchecked, it becomes checked and if it is already checked it becomes unchecked. For how ...
55 views

Expected samples to observe all unique observations

Suppose I have a bag with: $6$ red balls $4$ blue balls $1$ black ball If I sample one ball from the bag at a time, with replacement, what is the expected number of samples required before I observe ...
45 views

What is the expected number of cards I should buy to have all of them? [duplicate]

Background:My little brother collects cards and tries to complete a book of them, In order to depress him a little I'm trying to compute the number of he need to buy in order to collect all of them,...
42 views

Different ways to calculate the expected value of getting all faces of a 6 sided die atleast once

Problem Statement: You roll a fair six-sided die until all six numbers have been rolled at least once. What is the expected value of that ? Can you write different ways to solve this problem ?
Let T denote the number of times we have to roll a fair dice before each face has appeared at least once and N denote the number of different faces appearing in the first six rolls. Then $E(T|N=3)=?$ ...
Suppose that I have $N$ distinct objects, each of which have $1/N$ chance of being drawn. What is the expected number of draws, $D$, to draw at least $x$ of each object (with replacement)? For example:...