P(g(X) > c) using inverse transformation

Questions requiring probability calculations P(Y > c) where Y = g(X), solved by finding the equivalent condition on X (e.g., solving inequalities involving X² or √X) and using the uniform CDF.

1 questions

Edexcel FS2 AS 2024 June Q4
  1. The continuous random variable \(X\) is uniformly distributed over the interval [2, 7]
    1. Write down the value of \(\mathrm { E } ( X )\)
    2. Find \(\mathrm { P } ( 1 < X < 4 )\)
    3. Find \(\mathrm { P } \left( 2 X ^ { 2 } - 15 X + 27 > 0 \right)\)
    4. Find \(\mathrm { E } \left( \frac { 3 } { X ^ { 2 } } \right)\)