# Définition Distribution function

The distribution function describes the dependence between a random variable and its probabilities, i.e. it indicates the probability with which a random variable takes a specific value.

Example:

A football player is injured during training. Based on experience, it takes between 2-7 days for him to recover and be able to play again. The random variable describes the number of days until recovery. With each day, the probability of recovery increases:

 Days (x) Probability of recovery x > 2 0 x > 3 0.05 x > 4 0.2 x > 5 0.55 x > 6 0.9 x  ≥  6 1

As can be seen in the table, the football player will recover on day 5 with a probability of 90% (i.e. he might recover earlier than that).

Mathematically, the distribution function is the integral of the density function. Possible kinds of distribution functions are the normal distribution, the uniform distribution or the binomial distribution

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