The discrete uniform distributionEdexcel International A Level Maths: Subtopic test

1. 1
   A fair eight-sided spinner has faces numbered 1 to 8. The random variable $X$ is the number on the face it lands on.

   (a)

   Find $\mathrm{P}(X\ge6)$.

   [1 mark]

   • A$\frac{5}{8}$
   • B$\frac{1}{4}$
   • C$\frac{3}{8}$
   • D$\frac{1}{2}$

   (b)

   Find $\mathrm{E}(X)$.

   [1 mark]

   • A$4.5$
   • B$4$
   • C$9$
   • D$36$

   (c)

   Find $\mathrm{Var}(X)$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The discrete random variable $Y$ takes each of the values $1, 2, \ldots, n$ with equal probability, and $\mathrm{E}(Y)=7.5$.

   (a)

   Find the value of $n$.

   [1 mark]

   • A$15$
   • B$16$
   • C$13$
   • D$14$

   (b)

   Find $\mathrm{P}(Y>10)$.

   [1 mark]

   • A$\frac{5}{14}$
   • B$\frac{3}{14}$
   • C$\frac{2}{7}$
   • D$\frac{5}{7}$

   (c)

   Find $\mathrm{Var}(Y)$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A fair ten-sided spinner has faces numbered 0 to 9. The random variable $X$ is the number on the face it lands on.

   (a)

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

   [3 marks]

   (b)

   Find the probability that $X$ lies within one standard deviation of its mean.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   The discrete random variable $X$ takes each of the values $1, 2, \ldots, n$ with equal probability, and $\mathrm{Var}(X)=14$.

   (a)

   (i) Show that $n=13$.
   (ii) Find $\mathrm{E}(X)$.
   (iii) Find the probability that $X$ is greater than one standard deviation above its mean.

   [6 marks]

   (b)

   A second discrete random variable $W$ takes each of the values $1,2,\ldots,m$ with equal probability, where $m$ is a positive integer. Given that $\mathrm{Var}(W)>\mathrm{Var}(X)$ and $\mathrm{E}(W)<10$, find all the possible values of $m$.

   [6 marks]

   Total for question 4: 12 marks

End of questions