def main():
results = relay.ReadResults()
speeds = relay.GetSpeeds(results)
speeds = relay.BinData(speeds, 3, 12, 100)
# plot the distribution of actual speeds
pmf = thinkstats2.Pmf(speeds, 'actual speeds')
# plot the biased distribution seen by the observer
biased = ObservedPmf(pmf, 7.5, label='observed speeds')
thinkplot.Pmf(biased)
thinkplot.Save(root='observed_speeds',
title='PMF of running speed',
xlabel='speed (mph)',
ylabel='PMF')
cdf = thinkstats2.Cdf(pmf)
cdf_biased = thinkstats2.Cdf(biased)
thinkplot.PrePlot(2)
thinkplot.Cdfs([cdf, cdf_biased])
thinkplot.Save(root='observed_speeds_cdf',
title='CDF of running speed',
xlabel='speed (mph)',
ylabel='CDF')
# # As a result, runners were spread out along the course with little relationship between speed and location. When I joined the race, the runners near me were (pretty much) a random sample of the runners in the race. # # So where does the bias come from? During my time on the course, the chance of overtaking a runner, or being overtaken, is proportional to the difference in our speeds. I am more likely to catch a slow runner, and more likely to be caught by a fast runner. But runners at the same speed are unlikely to see each other. # # Write a function called `ObservedPmf` that takes a `Pmf` representing the actual distribution of runners’ speeds, and the speed of a running observer, and returns a new `Pmf` representing the distribution of runners’ speeds as seen by the observer. # # To test your function, you can use `relay.py`, which reads the results from the James Joyce Ramble 10K in Dedham MA and converts the pace of each runner to mph. # # Compute the distribution of speeds you would observe if you ran a relay race at 7 mph with this group of runners. #%% import relay results = relay.ReadResults() speeds = relay.GetSpeeds(results) speeds = relay.BinData(speeds, 3, 12, 100) #%% pmf = thinkstats2.Pmf(speeds, 'actual speeds') thinkplot.Pmf(pmf) thinkplot.Config(xlabel='Speed (mph)', ylabel='PMF') #%% # Solution goes here #%% # Solution goes here #%%