Download RECITATION #2 22.02.2013 3.13. Let X be exponential with mean 1

RECITATION #2
22.02.2013
3.13. Let X be exponential with mean 1/λ, that is;
fX(x) = λ.e -λx
0<x <∞
Then find E[X|X>1].
3.15. The joint density of X and Y is given by
f (x, y) = e−y/y
0<x <y, 0<y <∞
Compute E[X2|Y = y].
3.17. (modified) The demand of an item at any month i, which is denoted by Di and Di is independent
and identically distributed random variable having mean µD and variance σD2. The lead time demand
of that item (in terms of months), which is denoted by L, is also a random variable having mean µLand
variance σL2. Then find the mean, µ and the variance σ2of the lead time demand.
3.74. There are five components. The components act independently, with component i working with
probability pi, i = 1, 2, 3, 4, 5. These components form a system as shown in Figure 3.7. The system is
said to work if a signal originating at the left end of the diagram can reach the right end, where it can
pass through a component only if that component is working. (For instance, if components 1 and 4
both work, then the system also works.) What is the probability that the system works?
Question 5 Norb and Diana enter a barbershop simultaneously. Norb will get a shave and Diana a
haircut. If the amount of time it takes to receive a haircut (shave) is exponentially distributed with
mean 1/λ1 (1/λ2) and if both Norb and Diana are immediately served, what is the probability that Diana
finishes before Norb? See the result for the case where 1/λ1=20 and 1/λ2=15.