Recall that a gap penalty score is the log probability of a gap of a specified length. Answer parts a. and b. for the cases of both linear- and affine-gap penalties. 

a. Show that the probability density function, p(g) for a gap of length has the form p(g)=k.10^-λg where k and lambda are constants. 

b. Is the distribution of gap lengths p(g), properly normalized? If not, is it possible to normalize this distribution? Explain how.