A mathematical model in political science* asserts that the length of time served (continuously) by a legislator is a random variable X that is exponentially distributed with density function

where t is the number of years of continuous service and c is a positive constant that depends on the nature and character of the legislative body. 

a. For the U.S. House of Representatives, it was found that c = 0.0866. Find the probability that a randomly selected House member will serve at least 6 years.

b. For the British House of Commons, it was found that c = 0.135. What is the probability that a member of this body will serve at least 6 years?

Transcribed Image Text:

N(t) = -ct [ce lo for t≥ 0 for t < 0