Browsing All Posts filed under »measures«

Sampling until you get all six

June 4, 2013


A common problem goes like this: There are six different Famous Statistician cards, one (randomly) in each box of Chocolate Sugar Bombs. How many boxes do you need to buy to get all six? This is a good three-collection simulation in Fathom, and uses two little-used features, sample until and the uniqueValues( ) function. Make […]

Using summary tables in simulations

August 17, 2012


In the apstat community thingy, Rudy Medina posted a problem, and Paul Myers posted a solution. I’ll show another solution, and maybe veer off into philosophy. Here’s the problem (from 16 August 2012): A bus stop has 7 stops and 4 passengers.  If every passenger is equally likely to get off at any stop, what is […]

Streak Lengths

August 14, 2012


We humans see streaks as indications of non-randomness, but streaks do occur in genuine random phenomena—usually more than we think. There are famous activities about this, like the one where you ask students to (secretly) create “realistic” sequences of 100 heads-or-tails coin flips along with genuine sequences from a fair coin. The wise, omniscient teacher […]

Sampling Without Replacement: Lottery Problem

June 14, 2012


Yay! A request! From Ben Ceyanes on the APstat listserve: Ok, So I am brand new to fathom and to AP Stats this year and I am getting frustrated trying to figure out how to simulate a problem on fathom.  The problem says that a person buys 5 lottery tickets with 6 numbers ranging 1 to […]

The Key to the Birthday Problem: uniqueValues( )

May 30, 2012


It’s a famous probability problem: given N people in a room, what’s the probability that at least two of them share a birthday? It’s famous because the answer is often surprising: a remarkably small number (23) will give you a probability over 50%. How do you simulate it in Fathom? The key is going to be […]

Random Walk

May 26, 2012


The random walk is a thought experiment (we hope) that underpins a lot of formal statistics and error analysis. The idea is that for every step, you flip a coin. Heads, you move forwards; tails, you move back. You take a total of n steps. How far are you likely to travel? If you’re experienced […]

Exponential Decay Simulation

May 9, 2012


This comes from a Fathom listserv query by David Petro: 1. Flip 1000 coins 2. Remove the heads and count up the tails 3. Flip the remaining tails again 4. Repeat 2 & 3 until no coins remain 5. Graph the number of tails after each experiment. This is what I have tried I Have […]