Lecture 2: Binomial & Poisson Distribution

In this lecture, we learnt three concepts: expectation, variance and mode

Expectation is the mean (average) value of the random variable after a large number of trials.

Variance is about the spread of the data, i.e. the larger the variance, the more likely that you will get a outcome that is far away from the expectation.

Mode is the value that is most likely to occur.

To do a question in Binomial distribution, you have to take note of the following:

• define the random variable first
• check that it does follow Binomial distribution
• find out what is the value of n (no. of trials) and p (probability of success)
• understand what the question is asking about and use G.C. to solve the problem

You can attempt all the questions in tutorial 14A after this lecture.

For enrichment: \[E(X)=\sum_{k=1}^{n}P(X=X_{k})X_{k}\]

\[Var(X)=\frac{1}{n}\sum_{k=1}^{n}P(X=X_{k})(X_{k}-E(X))^{2}\]

Challenging question: For a game, you have a probability of 0.5 to win 2 dollars, 0.4 chances to win 3 dollars and 0.1 chances to win 10 dollars. If you need to pay 3.5 dollars to play the game, would you want to play?