204 views

### Problem about number of trials until first success [duplicate]

The problem is like this: A standard deck contains $52$ cards, $4$ each of $2,3,4,5,6,7,8,9,J,Q,K,A$. Now start the following process. Pick a random card from the deck, show it, and then return it to ...
122 views

### Average number of stickers to complete an album [duplicate]

Suppose I have a sticker album which consists of $N$ stickers. How many stickers should I buy in average to complete this album, assuming all the stickers appear with the same frequency? More ...
119 views

### Expected values of Cereal box - Linearity of expectation puzzle [duplicate]

A toy is randomly put in a given Cereal box as a promotional gift. There can be N different types of toys and each one can be of any type N (IID). (a) Find the expected number of cereal box one has to ...
77 views

### If I'm sampling from N items, how many samples are needed to get all N items at least once? [duplicate]

I have a situation where I have N items in the population (e.g. these are item IDs in some inventory). Suppose I can sample and get back 1 item at a time, where each item has an independent and ...
56 views

### What is the probability distribution for this question? [duplicate]

I tried to find the probability distribution for this problem and then calculate the expectation of $n$. I suppose the total states of our problem would be $52^n$ and our desired states would be $52$ ...
84 views

### Average # of tracks that must be heard on a CD, whose player's shuffle function can play the same song >1×, before all tracks of CD heard. [duplicate]

Suppose you have a CD of $n$ tracks. Your CD player's shuffle function is broken; it selects a random song, possibly even the one(s) already played, before all tracks are played. How many tracks (...
84 views

### 4 Distinct toys in cereal boxes, on average, how many do I need to open to get all the toys? [duplicate]

here's my question: There are 4 distinct toys in cereal boxes, and each type, independent of prior selections, is equally likely to be in a box. On average, how many cereal boxes would you need to ...
108 views

### Random but very interesting probability question! [duplicate]

There are 100 types of cards, each type with a number from 1 to 100 on it. Each minute I am given a random card. Random means that the number of my card has an equal chance of being 1,2,3,...,100. I ...
78 views

### $x_1,x_2,\dots,x_n$ are i.i.d RVs uniformly distributed on $\{1,2,\dots,N\}$. [duplicate]

Let $x_1,x_2,\dots,x_n$ be independent identically distributed random variables uniform on $\{1,2,\dots,N\}$, and let: $Y_n:=\text{the number of different elements in } \{x_1,x_2,\dots,x_n\}$. Let \$T:...
63 views

### Taking balls from a bag with replacement [duplicate]

Possible Duplicate: Expected time to roll all 1 through 6 on a die This is not a homework question. This question is spurred by me thinking about card collecting games (maybe baseball cards, ...
58 views

### Expected number of rolls until all die faces have appeared? [duplicate]

Suppose you have a die. On average, how many rolls does it take for all the faces (1 through 6) to have appeared? Also, what kind of distribution is this? (I thought of this question when watching ...
41 views

### Find expectation of a probablity distribution [duplicate]

There're k balls in a bag, each one with a different colour. Draw one ball from the bag randomly each time, then put the ball back. Let random variable X = the number of balls to draw until all k ...
46 views

### Probability: finding the expectation of “overlapping events” [duplicate]

Suppose there are 666 coins with 6 different colors in a non-transparent box. 111 of them are white coins. 111 of them are black coins. 111 of them are yellow coins. 111 of them are red coins. 111 of ...