a=2 b=8

The experiment consists in shooting a bow at the target twice. The targed consists of three rings (I, II, III). The hit probability for ring I is 0.25 for ring II is 0.6 and for ring III is 0.15. Hits are scored respectively: I for 2a points, II for 6 points and the third for b points. Let the random variable X be the sum of the points after two shots. Determine the probability mass function of the random variable X (and explain all the probabilities), Determine the cummulative distribution function of the random varialbe X, Draw graphs of p.m.f. and c.d.f. Compute the expected value and the standard deviation of X