Answer Happy

On the exam 2 review, we saw that the exponential distribution has the property that it is memoryless that is P(X > a +b | X > a) = P(X > b) for two positive constants a and b. We will now show that the Weibull distribution does not have this property in general, but does for one very specific parameter value. a. Find P(X > a+b | X > a) where X has the Weibull distribution with parameters a and B. b. Find P(X > b) where X has the Weibull distribution with parameters a and B. C. For what specific value of a are your answers for (a.) and (b.) equal? Why are these not equal for every other value of a? Notice that for the specific a value where these are equal, the Weibull reduces to the exponential distribution, so this shouldn't be too surprising.