Discrete probability distributions questions

Questions to attempt

3 questions on Discrete probability distributions, each with its mark scheme and worked method. Reveal the answer when you have had a go.

1. FS1-1.1 · Calculation of the mean and variance of discrete probability distributions. Extension of expected value function to include E(g(X)).

   Q1

   ORIGINAL

   Year 1

   Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.

   1.

   The random variable $X$ takes values $-2,1,3$ with probabilities $0.2,0.5,0.3$ respectively. Calculate $E[(X+2)^2]$.

   (4)

   (Total for Question 1 is 4 marks)

   Reveal answer and method

   Report this question

   Ask Oscar about this question

2. FS1-1.1 · Calculation of the mean and variance of discrete probability distributions. Extension of expected value function to include E(g(X)).

   Q2

   ORIGINAL

   Year 1

   Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.

   2.

   The random variable $X$ takes values $0,1,2,4$ with probabilities $0.15,0.25,0.35,0.25$ respectively. Find $E(X)$ and $\operatorname{Var}(X)$.

   (4)

   (Total for Question 2 is 4 marks)

   Reveal answer and method

   Report this question

   Ask Oscar about this question

3. FS1-1.1 · Calculation of the mean and variance of discrete probability distributions. Extension of expected value function to include E(g(X)).

   Q3

   ORIGINAL

   Year 1

   Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.

   3.

   The random variable $X$ takes values $0,1,3,5$ with probabilities $k,2k,3k,4k$ respectively. Find $k$, $E(X)$, $\operatorname{Var}(X)$ and $E[(X-2)^2]$.

   (7)

   (Total for Question 3 is 7 marks)

   Reveal answer and method

   Report this question

   Ask Oscar about this question

Progress is saved on this device for guests and accounts right now; cross-device account sync is not live yet.

FS1-1 Discrete probability distributions revision notes