Edexcel S1 — Question 4

Exam BoardEdexcel
ModuleS1 (Statistics 1)
TopicDiscrete Probability Distributions
TypeOne unknown from sum constraint only
4. The discrete random variable \(X\) has the following probability distribution :
\(x\)012345
\(\mathrm { P } ( X = x )\)0.110.170.20.13\(p\)\(p ^ { 2 }\)
  1. Find the value of \(p\).
  2. Find
    1. \(\mathrm { P } ( 0 < X \leq 2 )\),
    2. \(\mathrm { P } ( X \geq 3 )\).
  3. Find the mean and the variance of \(X\).
  4. Construct a table to represent the cumulative distribution function \(\mathrm { F } ( x )\).
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