Probability Theory - Assignment A #
Exercise 1 (2 x 12.5 points) #
A data scientist develops a model of the mortality probability distribution function
is 0.0 outside the above range of .
a. What is the probability that a person will die between 60 and 70.
b. What is the probability that a person will die between 60 and 70, given that was alive at 60.
Exercise 2 (2 x 12.5 points) #
Three switches connected in parallel operate independently. Each switch remains closed with probability .
a. Find the probability of receiving an input signal at the output.
b. Find the probability that switch is open given that an input signal is received at the output.
Exercise 3 (2 x 12.5 points) #
Make yourself familiar with the multinomial distribution
a. Each trial involves throwing a die with 10 faces/sides. All faces are equally probable aka the die is not biased. Calculate the probability of the counts of outcome “2” if we performed trials.
b. Simulate n independent trials of the multinoulli (categorical distribution) compliant to the specification of (a). Plot the probability in (a) as a function of n independent trials (n=10-1000). Write your conclusions with respect to the behavior of the estimated probability as increases.
NOTE: Submit this exercise in a colab notebook with permissions set to the professor and grader to be able to view.
Exercise 4 (25 points) #
Replicate the Figure 1 plots of this writeup.
NOTE: Submit this exercise in a colab notebook with permissions set to the professor and grader to be able to view.