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In this first grade lesson, we will also cover the concept of equiprobability, the expectation and standard deviation and the variance of a random variable.
I. Random variables and probabilities
Let be the finite universe of a random experiment.
A random variable X on is a function which, to each outcome of , associates a real number.
Let X be a random variable taking the values . If for each value , we associate the probability of the event , we define the probability law X.
The probability law of a random variable is presented in the form of a table.
We have .
II. Expectation, variance and standard deviation.
Let X be a random variable taking the values with the respective probabilities .
- We call the expectation of X the number .
- We call the variance of X the number
- We call the standard deviation of X the number .
III. Affine transformation of a random variable.
Let X be a random variable taking the values . For all real a and b, we can define another random variable, by associating to each outcome
giving the value , the number .
We note this random variable aX+b.
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