Home » VCE » Maths Methods U3 & 4 Master Notes » Conditional Probability

Conditional Probability

3.1 Continuous Probability Distribution and Density Function

Continuous Probability Distributions

  • The probability distribution for a continuous random variable is a description all the possible values of the random variable, and its corresponding probability.
  • Unlike discrete random variables which takes on a set of individual values, a continuous random variable is one that can take any value in an interval of the real number line.

For example, X is a continuous random variable if it takes on any variable in the interval [-0.005,0.005]. In this case, X might be the standard error when measuring using a micrometer screw gauge.

  • A continuous random variable has no limit as to the accuracy with which it can be measured. Using the example above, we can have
Read More »3.1 Continuous Probability Distribution and Density Function

1.2 Introduction to Probabilities


  • Probability is a numerical measure of the chance of a particular event occurring.
  • It is defined that the sum of probabilities of all possible outcomes to be 1, and all individual probabilities is non-negative. To sum up, the probability of each outcome is a real number in the interval [0,\ 1].
  • The probability of an event is equal to the sum of the probabilities of the outcomes in that event.
  • Mathematically, we represent probability of an event as \operatorname{Pr}(X=x) or \operatorname{Pr}(x), which X is the criteria to be observed, and x is the (actual) possible outcome.
  • Usually, we assume that each outcome is equally likely to happen i.e. have the same probability, unless there are conditions/evidence that says otherwise. Thus, if there are n equally likely outcomes, probability of each event is \frac{1}{n}.
Read More »1.2 Introduction to Probabilities