How do you find an unknown constant in a distribution?

Set the sum of all probabilities to 1 and solve.

What is a discrete uniform distribution?

n values, each with probability \frac1n.

Is the total of two fair spins uniform?

No; some totals can be made in more ways than others.

How do you find P(sum=s) for two independent values?

List all pairs giving s, multiply each pair's probabilities and add.

Why are (1,2) and (2,1) counted separately?

They are different outcomes, each with the same probability.

Probability of exactly one of two events, for mutually exclusive values?

Add the separate probabilities.

Is the mean or variance required for this topic?

No; calculation of mean and variance is excluded.

Discrete probability distributionsEdexcel A-Level Maths: Flashcards

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What is a discrete random variable?

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What is a discrete random variable?: A variable taking separate values, each with a probability.
What must the probabilities of a discrete distribution sum to?: $1$
Range of every $P(X=x)$ ?: Between $0$ and $1$ .
How do you find an unknown constant in a distribution?: Set the sum of all probabilities to $1$ and solve.
$P(X=x)=kx$ for $x=1,2,3,4$ : value of $k$ ?: $10k=1$ , so $k=\frac1{10}$ .
How is $P(X\ge3)$ found for values 1 to 4?: $P(X=3)+P(X=4)$
What is a discrete uniform distribution?: $n$ values, each with probability $\frac1n$ .
Fair 8-sided die: $P(X=5)$ ?: $\frac18$
Is the total of two fair spins uniform?: No; some totals can be made in more ways than others.
How do you find $P(\text{sum}=s)$ for two independent values?: List all pairs giving $s$ , multiply each pair's probabilities and add.
Why are $(1,2)$ and $(2,1)$ counted separately?: They are different outcomes, each with the same probability.
Probability of exactly one of two events, for mutually exclusive values?: Add the separate probabilities.
Is the mean or variance required for this topic?: No; calculation of mean and variance is excluded.

Exam questions on Discrete probability distributions

The discrete random variable $X$ has probability distribution $P(X=x)=kx$ for $x=1,2,3,4$ , where $k$ is a constant.
Two independent values of $X$ are observed. Find the probability that their sum is 3.2 marks
A fair eight-sided die has faces numbered 1 to 8. The random variable $X$ is the score when the die is rolled once.
The die is rolled twice. Find the probability that the first score is greater than the second.2 marks
The discrete random variable $Y$ takes the values 0, 1, 2 and 3, with $P(Y=0)=0.15$ , $P(Y=1)=a$ , $P(Y=2)=2a$ and $P(Y=3)=a+0.05$ .
Find the value of $a$ and hence $P(Y\ge2)$ .3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).