1. Let X~Pois(1) what is the variance of X given x is bigger than 0?

a. (e-2)/(e-1)

b. e/(e-1)

c. 1/(e-2)

d. e(e-2)/(e-1)^2

I've tried to use the conditional variance formula but I had problems with calculating the

probability of x=k and x>0.

2. A worker calls his wife once a day. the length of each talk is independent of the others, its a random variable which distributes exponentially with a mean of 5.

One day the boss tells the worker that it is unacceptable and he has 3 more chances, if he calls his wife and talks for more than 10 minutes 3 times he will be fired.

What is the expected number of days the worker has before he gets fired?

a. 2e^3

b. 3e^3

c. 3e^(-2)

d. e^2 + e^3

The parameter of the exponential distribution is 1/5... this is easy.

but I have no idea what should I do next.