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Suppose that you have a pool of n different types of coupons (one of each) and want to sample k coupons with replacement. What is the distribution of the random variable X, which counts the number of distinct coupons observed with each k-sized sample? I was unable to come up with a closed-form solution on my own, instead resorting to simulation and brute force. This captures a solution I was able to find by searching online and putting the pieces together. I've written the equations below in approximate Wolfram language syntax, since math typesetting is not available.

Related problems

bsidhom

#!/usr/bin/env bash

set -euo pipefail

function main() {
  local input="$1"
  local output="$2"
  local timestamp="$3"

  if [[ "$input" == "$output" ]] ; then

bsidhom

#!/usr/bin/env python3

# Update video timestamps to match timestamp metadata in associated JSON files.

import asyncio
import datetime
import json
import os
import os.path
import subprocess

bsidhom

#!/usr/bin/env bash

set -euo pipefail

readonly TIME_ZONE="${TIME_ZONE:-America/Los_Angeles}"

function main() {
  local file="$1"
  local timestamp
  timestamp="$(extract_timestamp "$file")"

bsidhom

#!/usr/bin/env python3

import argparse
import asyncio
import concurrent.futures
import functools
import time
import typing

import aiohttp

bsidhom

#!/usr/bin/env python3

import argparse
import asyncio
import os
import sys


async def main():
    parser = argparse.ArgumentParser("Createa a child process")

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bsidhom

#!/usr/bin/env python3

# Exact anagram finder. We start with a target name ("vilepechora") and consider
# all two-name exact anagrams of this target. Specifically, we do not consider
# anagrams of subsets of the original character set. We consider first and last
# names as different types to narrow the search space (there are 1712 matches if
# you consider first and last names to be interchangeable). There are "only" 582
# matches by considering first and last names separately (based on which dataset
# they're found in).

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