: On average, an electronic device lasts seven years. The length of the time that this device

lasts is exponentially distributed.

a$.$ What is the variance of the time that tihs device lasts? Calculate the variance using the pdf$.$

b$.$ What is the probability that this device will last less than $9$ years?

c$.$ What is the probability that this device will last more than $7$ years?

d$.$ Given that this device lasts more than $7$ years, what is the probability that it will last less than

$9$ years?

e$.$ Eighty percent of these devices last at most how long?