What is a probability distribution?
Answer
A probability distribution lists all possible values of a random variable together with the probabilities of each value occurring.
The working
Definition
It describes how the total probability of 1 is distributed among the possible values of a random variable X.
Random variable
A random variable assigns a numerical value to each outcome of an experiment. For example, the number of heads in two tosses can be 0, 1 or 2.
Key condition
Each probability must satisfy 0 ≤ P(xᵢ) ≤ 1, and the sum of all probabilities must equal 1, that is, Σ P(xᵢ) = 1.
Mean of distribution
The mean or expected value is E(X) = Σ xᵢ P(xᵢ), the long-run average value of the random variable.
Example
For one fair coin toss with X = number of heads, P(X = 0) = 0.5 and P(X = 1) = 0.5, which sum to 1.
Stuck on something else?
Type your own doubt into the solver and get the full working in seconds — free, for physics, chemistry, maths and biology.
Open the solverRelated doubts