Probability Distribution, Glossary

Knowing the vocabulary of Probability Distribution precisely is worth easy marks in SPM Add Math. Questions often turn on a single keyword, read it correctly and the method follows; misread it and even good algebra earns nothing.

Because the SPM paper is bilingual (BM/EN), each term below shows the English and Malay wording, so your child recognises it whichever way a question is phrased.

• Random Variable, A random variable is a quantity whose value depends on the outcome of a random experiment, usually written with a capital letter such as $X$. For example, $X$ could be the number of heads when three coins are tossed. Each possible value has an associated probability. →
• Discrete Random Variable, A discrete random variable can take only separate, countable values, often whole numbers, with gaps between them. Examples include the number of goals in a match or the score on a die. Its probabilities are listed individually and must add up to one across all values. →
• Continuous Random Variable, A continuous random variable can take any value within an interval, including decimals, so its outcomes cannot be listed one by one. Examples include height, time, or mass. Because single values have zero probability, we work with probabilities over ranges, as in the normal distribution. →
• Probability Distribution, A probability distribution shows all the values a random variable can take together with their probabilities, as a table, graph, or formula. For a discrete variable the probabilities must sum to one. It lets us predict how likely each outcome is and calculate expected results. →
• Binomial Distribution, The binomial distribution models the number of successes in a fixed number of independent trials, each with the same probability of success $p$. Its probability is $P(X=r)={}^{n}C_{r}\,p^{r}(1-p)^{n-r}$, with mean $np$. Tossing a coin a set number of times is a classic example. →
• Normal Distribution, The normal distribution is a continuous distribution whose graph is a symmetric bell-shaped curve, centred on its mean $\mu$, with spread set by the standard deviation $\sigma$. Many natural measurements, such as heights, follow it approximately. The total area under the curve equals one, representing all probability. →
• Standard Normal Distribution, The standard normal distribution is a special normal distribution with mean $0$ and standard deviation $1$, written $Z$. Any normal distribution can be converted to it, which lets us use a single standard table of probabilities. This makes comparing different normal distributions straightforward. →
• Standard Score, A standard score, or $Z$-score, tells how many standard deviations a value lies from the mean, calculated by $Z=\frac{x-\mu}{\sigma}$. A positive score is above the mean and a negative one below. Converting to $Z$-scores lets probabilities be read from the standard normal table. →

Do not just memorise definitions, practise using each term inside a full solution, the way a marker expects to see it. In the Probability Distribution chapter especially, stating the right definition or condition in your working can itself earn a method mark.

Our teachers check that a student can both recall a term and deploy it fluently under exam conditions.

Vocabulary sticks best when it is tied to doing rather than reading. Instead of learning the Probability Distribution terms as a flat list, meet each one inside a worked question and say the step aloud in words as you write it, a term you can use in a sentence is a term you understand.

It also helps to link related terms together rather than in isolation, since Probability Distribution questions usually combine several ideas at once. Because the SPM paper is bilingual, glance once at the Malay and English wording of each term side by side, so the language a question is set in never throws you.

If a term keeps feeling slippery, that is usually a sign the underlying idea needs another look, not the word itself, and that is exactly the kind of gap a one-to-one lesson closes quickly.