9709 · 5.4
Discrete random variables — FAQ
Frequently asked questions for 9709 Discrete random variables. Direct answers first, then deeper explanation — then practise with marking.
What is the difference between a discrete and a continuous random variable?
A discrete random variable can only take specific, separate values (like integers 1, 2, 3...). You can count them. A continuous random variable can take any value within a given range (like a person's height, which could be 1.75m, 1.751m, 1.7512m...).
Why is the expectation E(X) sometimes a value that X can't actually take?
Expectation is the long-run average, not a guaranteed outcome. For a fair die, E(X) = 3.5. This means if you roll it thousands of times, the average of all your scores will be very close to 3.5. It's a theoretical central point of the distribution.
Is there an easy way to remember the variance formula?
Think of it as 'Mean of the squares minus the square of the mean'. In symbols, that's . This verbal cue helps many students remember the order and the squaring.
Can a probability in the distribution table be negative or greater than 1?
Absolutely not. A core rule of probability is that for any event A, . If you calculate a probability and it's outside this range, you have made a mistake. Similarly, the sum of all probabilities in your distribution must be exactly 1.