# 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

#### Step 1. Select the data source

Mathematical-based, simulated-data-based, or user data-based

#### Step 2. Set parameters

1. Set Parameters
• Mean = np
• Variance = np(1-p)
• From the example, we know n=10 (10 white blood cells), p=0.2 (the probability of any cell being a lymphocyte)

2. Change Observed Data

The observed number is 2 lymphocytes

When the number of bins is 0, plot will use the default number of bins

Data point can be separated by , ; /Enter /Tab /Space

Data be copied from CSV (one column) and pasted in the box

Missing value is input as NA

Upload data will cover the example data

2. Show 1st row as column names?

3. Use 1st column as row names? (No duplicates)

Correct separator and quote ensure the successful data input

Find some example data here

When the number of bins is 0, plot will use the default number of bins

#### 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?

#### Step 1. Select the data source

Mathematical-based, simulated-data-based, or user data-based

#### Step 2. Set parameters

1. Set Parameters

From the example, the rate is 2.3 and the duration of the rate is 12 months

2. Change Observed Data

The observed is <= 5, and we wanted to know the cumulated probability after 5 months, which means 1 - cumulated probability of 0-5 months

When the number of bins is 0, plot will use the default number of bins

Data point can be separated by , ; /Enter /Tab /Space

Data be copied from CSV (one column) and pasted in the box

Missing value is input as NA

Upload data will cover the example data

2. Show 1st row as column names?

3. Use 1st column as row names? (No duplicates)

Correct separator and quote ensure the successful data input

Find some example data here

When the number of bins is 0, plot will use the default number of bins

#### 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