1. A. Which distribution fits each of these random variables. 1
A. Which distribution fits each of these random variables? 1. Number of heads in 20 tosses of a coin 2. Number of punctures per month (if you're riding your bike at about the same rate, on about the same roads, with about the same quality of tyres) 3. Number of times the school server goes down per term 4. Variation of manufactured widgets from their design size 5. Number of bugs per thousand lines of computer code 6. Time to wait for a bus which runs exactly every 10 minutes (but you don't know the timetable) 7. Time to wait for a bus which runs about 12 times an hour, but randomly (without the bunching which happens in real life) 8. Lengths of rivers in metres 9. First digits of lengths of rivers in metres. B. Why do we quite often use a continuous distribution to describe a random variable which strictly speaking isn't continuous? 1

2. Discrete (result is a whole number: example, number of heads from tossing a coin)
Continuous (result can be anything over a range: example, size of error in manufacturing an item)
Small fixed number of trials
BINOMIAL
continuous random variable - NORMAL or CONTINUOUS UNIFORM DISTRIB or OTHER
Large fixed number of trials
POISSON APPROXIMATION TO BINOMIAL (if p is small). NORMAL APPROX (if p around 0.5, or for any p if n is big enough)
Over a continuous period of time
POISSON (or normal approx to Poisson if λ is big enough)
 continuous random variable - NORMAL or CONTINUOUS UNIFORM DISTRIB or OTHER
Binomial – variable takes only whole number values – like tossing coins
Continuity correction: if you use normal to approximate binomial or Poisson, then P(exactly n) is approximated by P(values which round to n), so P(10) is approximated by P(9.5<Y<10.5)
Normal – variable takes a continuous range of values. Like a range of heights in a population, or of errors in manufacturing
Poisson – variable takes only whole number values, but it’s the number of events over a continuous stretch of time. Like number of goals in a football match.
1/2/2019