Exercises for Lecture 9

9.10. Exercises for Lecture 9#

9.10.1. Exercise 9.1#

Write a program that generates pseudo-random numbers distributed according to an exponential function and stores them in a list.

9.10.2. Exercise 9.2#

Add to the previous program the source code that fills a histogram with the numbers present in the list where they have been transferred, and displays the histogram on the screen.

9.10.3. Exercise 9.3#

Write a program that plots the exponential probability distribution with a fixed parameter t₀.

9.10.4. Exercise 9.4#

Write a function likelihood that calculates the likelihood as the parameter t₀ varies, for a sample of pseudo-random events generated according to the instructions of Exercise 1.

How does the result depend on the number of events in the sample?

9.10.5. Exercise 9.5#

Write a function loglikelihood that calculates the logarithm of the likelihood as the parameter t₀ varies, for a sample of pseudo-random events generated according to the instructions of Exercise 1. Remember that the logarithm of the likelihood is defined only when the likelihood is strictly positive.

9.10.6. Exercise 9.6#

Study the behavior of the shape of the log-likelihood as a function of the number of events comprising the generated sample.