# Binomial Distribution

#### Functionalities

• Get a plot of Binomial Distribution B(n,p); n is the total sample size, p is the probability of success / event from the total sample; np=mean, np(1-p)=variance
• Get the probability of a certain position (at the red point)

#### Case Example

Suppose we wanted to know the probability of 2 lymphocytes of 10 white blood cells if the probability of any cell being a lymphocyte is 0.2

#### Mathematical-based Plot

Binomial probability plot

The blue curve is the normal distribution with mean n*p and sd n*p*(1-p). It indicates the normal approximation of binomial distribution.

Probability at the observed number of success /event (Red-Dot)

Explanation: the probability of 2 lymphocytes was about 0.03

#### Simulation-based Plot

Histogram from random numbers

Sample descriptive statistics

Sample descriptive statistics

# Poisson Distribution

#### Functionalities

• Draw a plot of Poisson Distribution P(Rate); Rate indicates the expected number of occurrences; Rate = mean =variance
• Get the probability of a certain position (at the red point)

#### Case Example

Suppose the number of death from typhoid fever over a 12 month period is Poisson distributed with parameter rate=2.3. What is the probability distribution of the number of deaths over a 6-month period?

#### Mathematical-based Plot

The blue curve is the normal distribution with mean=rate and sd=rate. It indicates the normal approximation of binomial distribution.

Poisson probability plot

Probability at the observed number of occurrences (Red-Dot)

Explanation: the probability distribution until 5 month was 0.97. Thus, the probability distribution after 6 months was about 0.03

Histogram from random numbers

Sample descriptive statistics