UMA028

Lecture (Lectures will be updated time to time. Please fetch the latest copy. Last updated on 01.09.25)

• Download Standard Normal Cumulative Probability Table  

• Download Practice Problems

Lab Experiments

1. Basics of MATLAB (Go to MATLAB onramp and attach the certificate of completion).

2.  (a) Write a code to generate geometric series and plot a histogram. The code should be generic. The user inputs the value of the common ratio.

 (b) Write a code to compute (N choose K) and K! The code should be generic.

3. Write a code to visualize birthday paradox. (The Birthday Paradox refers to the counterintuitive probability phenomenon that in a group of randomly chosen people, the likelihood of at least two individuals sharing the same birthday is surprisingly high. Assuming each birthday is equally likely among 365 days and independent of others, only 23 people are needed for the probability of a shared birthday to exceed 50%, and with 57 people, the probability exceeds 99%.)

4. Write a code of an experiment in which a die is thrown N times. Assuming that die is fair and plot the histogram of all events {1,2,3,4,5,6} for different values of N (say N=100, 1000, 10000, 100000). Show that the histogram becomes PMF as N tends to infinite.

5. Write a code to compute the expectation, variance and standard deviation of a dataset.

6. (i) Write a code to generate 1000 Bernoulli random variable and plot their PMF.

(ii) Write a code to generate 5000 Binomial random variables and plot their PMF.

(iii) Write a code to generate 1000 Geometric random variables and plot their PMF.

(iv) Write a code generate 5000 Poisson numbers and plot their PMF.

Hints to Experiments