A light fixture contains 2 light bulbs. The lifetime Xi of each bulb is exponentially distributed with a mean of 200 hours, i= 1,2,3. Suppose bulb lifetimes are independent from one another. Let T equal the time until a bulb in the fixture needs replacement.
a) What is the paramater Lamda of the exponential distribution?
b) What is the probability that X1 > 100 hours?
c) What is the expected value of X1?
d) What is the probability P(X1 > 100 and X2 > 100 and X3 > 100)?
e) What is the probability P(T > 100)?
f) If t is any positive number fine P(T > t)?
g) If t is any posivtive number fine P(T ? t)?