AQA S2 2007 January — Question 4

Exam BoardAQA
ModuleS2 (Statistics 2)
Year2007
SessionJanuary
TopicDiscrete Probability Distributions
TypeOne unknown from sum constraint only
4 The number of fish, \(X\), caught by Pearl when she goes fishing can be modelled by the following discrete probability distribution:
\(\boldsymbol { x }\)123456\(\geqslant 7\)
\(\mathbf { P } ( \boldsymbol { X } = \boldsymbol { x } )\)0.010.050.140.30\(k\)0.120
  1. Find the value of \(k\).
  2. Find:
    1. \(\mathrm { E } ( X )\);
    2. \(\operatorname { Var } ( X )\).
  3. When Pearl sells her fish, she earns a profit, in pounds, given by $$Y = 5 X + 2$$ Find:
    1. \(\mathrm { E } ( Y )\);
    2. the standard deviation of \(Y\).
This paper (8 questions)
View full paper
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8