OCR MEI AS Paper 2 2021 November — Question 6

Exam BoardOCR MEI
ModuleAS Paper 2 (AS Paper 2)
Year2021
SessionNovember
TopicDiscrete Probability Distributions
TypeOne unknown from sum constraint only

6 The probability distribution for the discrete random variable \(X\) is shown below.
\(x\)0123
\(\mathrm { P } ( X = x )\)\(3 p ^ { 2 }\)\(0.5 p ^ { 2 } + 2 p\)\(1.5 p\)\(1.5 p ^ { 2 } + 0.5 p\)
  1. Determine the value of \(p\).
  2. Determine the modal value of \(X\).