Maths with David

    9231. FS. Continuous Random Variables. Exam Questions

    9231/41/M/J/25q2

    (a) Show that a = 2/13 and find the values of b and c. [3 marks]

    (b) Find the mean of X. [3 marks]

    (c) Find the median of X. [2 marks]

    The random variable Y is defined by Y = X2.

    (d) Find the cumulative distribution function for Y. [4 marks]

    Mark scheme

    9231/43/M/J/25q3

    A continuous random variable X has probability density function f given by:

    f(x) = kx for 0 \leq x < 1 ,

    f(x) = k(8-x) for 1 \leq x < 8 ,

    f(x) = 0 otherwise, where k is a constant.

    (a) Show that k = \frac{1}{25} [2 marks]

    (b) Find the median value of X. [3 marks]

    The random variable Y is defined by Y = \sqrt[3]{X}

    (c) Find the probability density function of Y. [5 marks]

    Mark Scheme