Probability Distributions and Expected Value

Manual: General · Subject: Statistics

Understand how probabilities are distributed and how to find the average long-run outcome.

From outcomes to distributions

A probability distribution lists all possible values of a random variable and the probability of each value.

The expected value is the long-run average of a random process. For discrete values, $E(X)=\sum x_i p_i$

Example distribution

$E(X) = 0(0.2) + 1(0.5) + 2(0.3) = 1.1$

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Interpretation

Expected value does not always have to be a value that can actually occur; it is a weighted average.

What does a probability distribution describe?

Only the mean of data All possible values and their probabilities The largest value only A graph of categories only

What is the expected value of $X$ if $X$ is a fair coin toss coded as 0 for tails and 1 for heads?

Which formula gives expected value for discrete random variables?

E(X)=x/p

E(X)=\sum x_i p_i

E(X)=x_1+x_2

E(X)=p_1-p_2

In simple words, what is expected value?