Find cumulative distribution F(x)

A question is this type if and only if it asks to find or write down the cumulative distribution function F(x) = P(X ≤ x) for a discrete uniform distribution.

1 questions

Edexcel S1 2015 June Q6
  1. The random variable \(X\) has a discrete uniform distribution and takes the values \(1,2,3,4\) Find
    1. \(\mathrm { F } ( 3 )\), where \(\mathrm { F } ( x )\) is the cumulative distribution function of \(X\),
    2. \(\mathrm { E } ( X )\).
    3. Show that \(\operatorname { Var } ( X ) = \frac { 5 } { 4 }\)
    The random variable \(Y\) has a discrete uniform distribution and takes the values $$3,3 + k , 3 + 2 k , 3 + 3 k$$ where \(k\) is a constant.
  2. Write down \(\mathrm { P } ( Y = y )\) for \(y = 3,3 + k , 3 + 2 k , 3 + 3 k\) The relationship between \(X\) and \(Y\) may be written in the form \(Y = k X + c\) where \(c\) is a constant.
  3. Find \(\operatorname { Var } ( Y )\) in terms of \(k\).
  4. Express \(c\) in terms of \(k\).