Cambridge IGCSE Statistics 8: Probability distributions

Cambridge IGCSE Statistics 0479 Topic 8 requires learners to construct probability distributions for simple situations and calculate or use expectation. A distribution connects every possible value of a random variable to its probability, and its probabilities must total 1.

1. Random variables and possible values

A random variable assigns a numerical value to each outcome of a random process. It may count successes, record a score, or represent a monetary gain or loss. Use a clear symbol such as X and define what it measures.

Distinct outcomes can produce the same X-value. If two different spinner results both give a score of 3, combine their probabilities in the distribution row for X = 3. The distribution lists values, not necessarily every underlying outcome separately.

The values must be mutually exclusive and collectively exhaustive: exactly one listed value occurs in each trial, and no possible value is omitted.

2. Constructing a probability table

A discrete probability table normally has one row for x and one for P$X = x$. Generate the sample space systematically using a list, grid or tree, calculate the probability attached to each value, then combine equal values.

Check two conditions:

• every probability lies from 0 to 1 inclusive
• the sum of all probabilities equals 1

If a probability is represented by a parameter, use the total of 1 to solve it. Then verify the resulting values remain valid. An algebraic solution that makes a probability negative is not acceptable.

3. Deriving event probabilities from a distribution

Once the table is complete, add the probabilities for values satisfying the event. For example, P(X at least 2) includes X = 2 and every larger listed value. P(X below 2) excludes 2. Translate inequalities carefully before summing.

The complement can shorten work. P(X at least 1) equals 1 - P