Relationship between two random variables

A question is this type if and only if it defines one random variable Y in terms of another X (e.g., Y = aX + b) and asks to find properties of Y from properties of X.

1 questions

Edexcel S1 2022 January Q4
  1. The random variable \(W\) has a discrete uniform distribution where
$$\mathrm { P } ( W = w ) = \frac { 1 } { 5 } \quad \text { for } w = 1,2,3,4,5$$
  1. Find \(\mathrm { P } ( 2 \leqslant W < 3.5 )\) The discrete random variable \(X = 5 - 2 W\)
  2. Find \(\mathrm { E } ( X )\)
  3. Find \(\mathrm { P } ( X < W )\) The discrete random variable \(\mathrm { Y } = \frac { 1 } { W }\)
  4. Find
    1. the probability distribution of \(Y\)
    2. \(\operatorname { Var } ( Y )\), showing your working.
  5. Find \(\operatorname { Var } ( 2 - 3 Y )\)