| Exam Board | SPS |
|---|---|
| Module | SPS SM Statistics (SPS SM Statistics) |
| Year | 2022 |
| Session | February |
| Marks | 4 |
| Topic | Discrete Probability Distributions |
| Type | Piecewise or conditional probability function |
| Difficulty | Standard +0.3 This is a straightforward probability distribution question requiring basic probability axioms (sum to 1) and simple algebraic manipulation. Part (a) involves substituting x values and summing probabilities. Part (b) requires setting up one additional equation from the given condition and solving simultaneous equations. All steps are routine with no conceptual challenges beyond standard A-level probability. |
| Spec | 2.04a Discrete probability distributions |
\begin{enumerate}
\item Answer all the questions.
\end{enumerate}
The discrete random variable $X$ has the probability function
$$\mathrm { P } ( X = x ) = \left\{ \begin{array} { c c }
c ( 7 - 2 x ) & x = 0,1,2,3 \\
k & x = 4 \\
0 & \text { otherwise }
\end{array} \right.$$
where $c$ and $k$ are constants.\\
(a) Show that $16 c + k = 1$\\
(b) Given that $\mathrm { P } ( X \geq 3 ) = \frac { 5 } { 8 }$ find the value of $c$ and the value of $k$.\\[0pt]
\\
\hfill \mbox{\textit{SPS SPS SM Statistics 2022 Q11 [4]}}