Home page for accesible maths

Style control - access keys in brackets

Font (2 3) - + Letter spacing (4 5) - + Word spacing (6 7) - + Line spacing (8 9) - +

Coursework questions

  1. 1.

    The lifetime (in years) of a light bulb Y has a continuous distribution with probability density function

    fY(y)={yexp(-y2/2),y>0,0otherwise.
    1. (a)

      For a fixed y>0, find the probability the bulb survives at least time y.

    2. (b)

      Find the probability that the bulb’s lifetime is between one and two years.

    [2]

  2. 2.
    1. (a)

      Find the median x0.5 of the random variable XExp(λ) (i.e. with pdf fX(x)=λexp(-λx) for x>0 and fX(x)=0 otherwise).

    2. (b)

      Find x0.25 and x0.75 when X has probability density function fX given by

      fX(x)={8/(x+2)3,x>0,0otherwise.

    [4]

  3. 3.

    Let XU(0,1) be a uniformly distributed random variable with parameters 0 and 1. Let Z=-log(1-X), so that Z is a random variable taking values in (0,).

    1. (a)

      For arbitrary z>0, find P(Zz).

    2. (b)

      Find the probability density function of Z. What is the distribution of Z?

    [4]