Conditional probability
Conditional probability
If we have two random variables $X$ and $Y$ we can define the conditional probability that $X=x$ given that $Y=y$ as follows: $$ P(X=x|Y=y) = \frac{ P(X=x \wedge Y=y)}{ P(Y=y) } $$ If you have a pair of random variables $X$ and $Y$ then you can calculate the probabilty that $X$ takes on a particular value $x$ using: $$ P(X=x) = \sum_{i=0}^\infty P(X=x|Y=y_i)P(P=y_i) $$
Syllabus Aims
- You should be able to explain the definition of conditional probability.
- You should be able to explain in terms of conditional probability what it means when we state that two events are concurrent and what it means when we state that two events are mutually exclusive.
- You should be able to explain how the the probability that a random variable, $X$, takes on a particular value by using the probability mass function for a random variable $Y$ and a set of conditional probabilities of the form $P(X=x|Y=y)$. The second formula in the description above explains how this is done.
Description and link | Module | Author | ||
| Introductory material on conditional probability. | SOR3012 | J. F. McCann |
Description and link | Module | Author | ||
| Introduction to conditional probability | SOR3012 | G. Tribello | ||
| A video explaining the partition theorem in statistics | SOR3012 | G. Tribello |
Description and link | Module | Author | ||
| Exercises on conditional probability | SOR3012 | G. Tribello |
Contact Details
School of Mathematics and Physics,
Queen's University Belfast,
Belfast,
BT7 1NN
Email: g.tribello@qub.ac.uk
Website: mywebsite