(Solved): a) The discrete probability distribution is given by i. Show that \( m=\frac{1}{8} \) ii. Find the ...

a) The discrete probability distribution is given by i. Show that \( m=\frac{1}{8} \) ii. Find the mean of the probability distribution. iii. Calculate \( P(X>\mu) \) b) A bag contains 10 cards, of which 2 are marked two, 1 is marked three, 4 are marked four and 3 are marked five. i. Construct a probability distribution table, showing X, the number on the card. [2] ii. Use your table in i) to find the variance of this probability distribution. [3]