# Probability Distribution Table

These lessons, with videos, examples and step-by-step solutions, are suitable for A Level Maths students learning

• how to construct a probability distribution table for a discrete random variable,
• how to calculate probabilities from a probability distribution table for a discrete random variable,
• what is a cumulative distribution function and how to use it to calculate probabilities and construct a probability distribution table from it.

Constructing a Probability Distribution Table
This video shows you how to construct a probability distribution table for a discrete random variable.

Example:

1. Construct a table showing the probability distribution for the score on the spinner.
2. Construct a table showing the probability distribution for the winnings when throwing a six sided fair die at a charity fete.

Probability from a Discrete Probability Distribution Table
This video shows you how to calculate probabilities from a probability distribution table for a discrete random variable.

Example:
If the random variable X has the following distribution
Find
P(X > 3)
P(X < 2.5)
P(X < 6)

Probability : Cumulative Distribution Function F(X)
This tutorial shows you the meaning of this function and how to use it to calculate probabilities and construct a probability distribution table from it.

Example:
Cumulative Probability Function F(X)
F(x) = P(X) ≤ x)

If the random variable X has the following probability distribution the fimd F(3)

If F(1) = 0.2, F(2) = 0.9 and F(3) = 1 for a random variable X.
Construct a probability distribution table for X.

January 2008 Q7 (Probability)
Question 7:
Tetrahedral dice have four faces. Two fair tetrahedral dice, one red and one blue, have faces numbered 0, 1, 2, and 3 respectively. The dice are rolled and the numbers face down on the two dice are recorded. The random variable R is the score on the red die and the random variable B is the score on the blue die.
(a) Find P(R=3 and B=0).
The random variable T is R multiplied by B.
(b) Complete the diagram to represent the sample space that shows all the possible
values of T.
(c) The table represents the probability distribution of the random variable T. Find the values of a, b, c and d.
Find the values of
(d) E(T),
(e) Var(T).
7(a) Probability.

7(b)(c) Probability Distribution Table

7(d) Find E(X)

7(e) Find Var(X)

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