Discrete random variables

Sample questions

Original practice questions written in the style of the exam.

1. Question 16 marks

   The discrete random variable $X$ has probability distribution

   $x$	1	2	3	4
   $P(X = x)$	0.1	$k$	0.3	$2k$

   (a) Find the value of $k$.

   (b) Find $E(X)$ and $\text{Var}(X)$.

   (c) Find $E(3X - 2)$ and $\text{Var}(3X - 2)$.

   Mark scheme

   • (a) $0.4 + 3k = 1$, so $k = 0.2$ (1)
   • (b) $E(X) = 0.1 + 0.4 + 0.9 + 1.6 = 3$ (1)