Description
1 Definitions
1. The pmf for a Binomial Random variable Y ∼ (n, p) is given by
n!
pY (Y =k) = pk (1 −p)n−k , 0 ≤k≤n
k
2. The pdf of an Exponential Random variable X is given by (1.1)
pX (x) =ce−cxu(x)
2 Problems
1. Show that the solution of (1.2)
max pY (Y =k) p
is (2.1.1)
k
pˆ = n
2. Find (2.1.2)
Pr(X > T) (2.2.1)
where T is a constant.
3. If X represents the lifetime of a bulb, show that the value of c that maximizes the probability of k out of n bulbs working after T hours is
1 n
c= log (2.3.1)
T k
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