出自allan gut-probability P50 Exercise 4

The life T (hours) ofthe lightbulb in an overhead projector follows an Exp(10)-distribution. Duringa normal week it is used a Po(12)-distributed number of lectures lastingexactly one hour each. Find the probability that a projector with a newly installedlightbulb functions throughout a normal week (without replacing the lightbulb).

大意是：灯泡寿命服从参数为10的指数分布，使用时间服从参数为12的泊松分布，问在使用时间内灯泡不坏的概率？

请问各位大大，一个连续变量和一个离散变量的联合分布怎么求？

或者能否给出解题步骤？

谢谢。