# Probability

This app lets you study different probability distributions such as Binomial, Normal or Exponential. Input the distribution’s parameters and get the corresponding probabilities. It is organized in 3 steps:

1. Choice of probability distribution: select the probability distribution you want to perform your probability calculations, the normal distribution for example.
2. Choice of the parameters: type the values of the parameters of the probability density function, standard deviation and mean for example.
3. Calculate probabilities: define your bounds and calculate the corresponding probability or perform the inverse by typing a probability value to calculate the value of the corresponding bound.

Once you have made a choice and moved to the next step, you can return to the previous step by pressing back.

## First step: choosing the probability distribution

Select the probability distribution you want with the directional arrows. Then confirm by pressing OK to go to the next step.

You have the choice between 3 continuous distributions and 2 discrete distributions.

Continuous distributions:

• Uniform distribution
• Exponential distribution
• Normal distribution

Discrete distributions:

• Binomial distribution
• Poisson distribution

## Second step: choosing the parameters

Type the value of the parameter(s) then select the Next button and press OK to go to the next step.

At the bottom of the screen, you will see a description of the requested parameters.

In the table below, the parameters requested for each distribution are reminded.

Probability distribution Requested parameters What value to enter
Binomial ($n$, $p$) : number of trials and success probability (natural number, real number in $[0,1]$)
Uniform ($a$, $b$): bounds of the interval (real number, real number)
Exponential $\lambda$: parameter non-negative real number
Normal ($\mu$, $\sigma$): mean and standard deviation (positive real number, non-negative real number)
Poisson $\lambda$ :parameter non-negative real number

## Third step: calculating probabilities

### Calculating a probability

1. Select the bound in which you want to enter your value.
2. Type the value.
3. Confirm by pressing OK.

You can now read the result of the probability calculation.

### Modifying the bounds

You can modify the type of bounds for your probability calculations:

• $X≤a$
• $a≤X$
• $a≤X≤b$
• $X=a$

The last option only concerns discrete distributions.

To do so, follow the instructions below.

1. Select the Bound type icon at the top left of the screen and press OK.
2. A drop-down menu opens. Choose the type of bounds you want and confirm by pressing OK.

You have changed the type of bounds for calculating your probabilities.

### Calculating the inverse

You can calculate $a$ in $P(a≤X)=p$ from a given $p$ probability value.

1. Select the field in which the probability value is located.
The calculator will display the value of $a$.