AQA Paper 3 2021 June — Question 16

Exam BoardAQA
ModulePaper 3 (Paper 3)
Year2021
SessionJune
TopicDiscrete Probability Distributions
TypeTwo unknowns from sum and expectation

16 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.
16
  1. Show that \(16 c + k = 1\)
    16
  2. Given that \(\mathrm { P } ( X \geq 3 ) = \frac { 5 } { 8 }\) find the value of \(c\) and the value of \(k\).