Linked Questions

2
votes
1answer
538 views

Expected time to get all four unique coupons [duplicate]

Envelopes are on sale for Rs. 30 each. Each envelope contains exactly one coupon, which can be one of four types with equal probability. Suppose you keep on buying envelopes and stop when you collect ...
4
votes
0answers
96 views

Probability of observing all cards? [duplicate]

I have a stack of $n$ distinct cards. I randomly draw $N$ cards from the stack with replacement. Assume that $N \ge n$. What is the probability that I observe all cards at least once? I got this far:...
1
vote
2answers
55 views

Probability Problem [duplicate]

I have a question about a probability problem located here: http://www.statisticshowto.com/probability-and-statistics/probability-main-index/ And quoted here: “If you were trying to collect 6 ...
0
votes
0answers
45 views

How many random to get n unique integers [duplicate]

How many random integers from (1-n) must I produce to get all n integers Assume a perfect random Because of duplicates it will be more than n I understand there will be variance but is there an ...
1
vote
0answers
33 views

Expected value question [duplicate]

Say I am rolling a 20-sided die. What is the expected number of rolls to have rolled each number? I haven't taken statistics in a while so my syntax might be off but this question has been bugging me ...
41
votes
4answers
20k views

Generic sum of Gamma random variables

I have read that the sum of Gamma random variables with the same scale parameter is another Gamma random variable. I've also seen the paper by Moschopoulos describing a method for the summation of a ...
9
votes
6answers
3k views

What are the chances rolling 6, 6-sided dice that there will be a 6?

More generally, what is the probability that n n-sided dice will turn up at least one side with the highest number ("n")? My crude thinking is that each side has 1/6 probability, so that 6 ...
15
votes
2answers
818 views

Expected number of times to roll a die until each side has appeared 3 times

What is the expected number of times you must roll a die until each side has appeared 3 times? This question was asked in primary school in New Zealand and it was solved using simulations. What is ...
8
votes
1answer
736 views

Probability to draw a black ball in a set of black and white balls with mixed replacement conditions

When a black ball is drawn, it is not replaced in the set, but white balls are replaced. I have thought of this, with the notations: $b$, $w$ the initial number of black and white balls $x_i = (b - ...
1
vote
0answers
578 views

How can I sample from a multinomial distribution with a fixed expected number of remaining categories?

I have a population of entities associated with different categories, say blue 50000 red 300 green 80 yellow 10 pink 6 orange 3 white 2 The ...
3
votes
2answers
82 views

Expected of number of discrete uniform variables whose sum is bigger than k (from characteristic function of discrete Irwin–Hall distribution?)

The problem Imagine we keep uniformly drawing $n$ integers $X_i$ from {0, 1, ..., 9} so that their sum is more than $10$. For instance, one draw would be {1, 0, 2, 5, 3}, hence $n=5$, and repeat this ...
1
vote
1answer
254 views

Is X a negative binomial? ( Tosses of dice)

Two dice are tossed independently until each pair has appeared at least once. Find the expected number of tosses needed and the standard deviation of this number of tosses. My attempt Let X be the ...
3
votes
1answer
151 views

How Many Random Choices Before They Have All Been Picked About The Same # Of Times?

Given a set of numbers 1 through N, how many times do I have to randomly pick a number before all of the numbers have been picked a roughly equivalent (within 5% of each other) amount of times, and ...
2
votes
0answers
136 views

Intuition about a coupon problem were we ask for the distribution of the unique coupons when the number of draws is fixed

Alternative viewpoint of the coupon collectors problem In the coupon collectors problem we draw from a collection of $n$ coupons, with replacement and ask the question how many draws $K$ it takes to ...
3
votes
1answer
76 views

How many samples do I need to take to expect I have seen (x%, say 99%) of the finite population?

Let's say I have balls numbered 1 to 100 in an urn. Every time I pick one at a random, record it as seen and put it back in the urn. How many such picking do I have to perform if I expect to see at ...

15 30 50 per page