Lesson 7 exercises¶

Exercise 7.1¶

What is the plug-in principle and how is it used in non-parametric statistics?

Exercise 7.2¶

What is a bootstrap sample and what is a bootstrap replicate?

Exercise 7.3¶

Consider the following data set for waiting times in minutes for nuclear localization events of the gene MSN-2 in yeast (these are real measurements done by Yihan Lin in Michael Elowitz’s lab).

[1]:

t = [3, 6, 11, 5, 5, 4, 73, 31, 7, 6,
     30, 4, 32, 30, 5, 53, 2, 15, 18,
     14, 3, 49, 7, 4, 4, 2, 9, 11, 8,
     5, 14, 6, 32, 40, 3, 5, 24]

You suspect that MSN-2 localization may be a Poisson process and therefore that these waiting times are Exponentially distributed with a characteristic wait time of 15 minutes. Do a quick graphical analysis to check out this idea. Also compute a point estimate for the mean waiting time and a 95% confidence interval for it.

Exercise 7.4¶

Write down any questions or points of confusion that you have.