Assignment 3
Due date: 11 February 2010
Total number of points: 25
Q
1.
Suppose that the random variable
X
has the following cumulative distribution function CDF:
F
X
(
x
) =
0
,
x
≤
0
x
3
,
0
≤
x
≤
1
1
,
x
≥
1
.
(a)
Compute
P
(
X >
0
.
5) and
P
(0
.
2
< X <
0
.
8).
(b)
Find the probability density function of
X
.
(c)
Find E[
X
] and Var[
X
].
Q
2.
Assume that arrivals of small aircrafts at an airport can be modeled by a Poisson process with average 1 aircraft
per hour.
(a)
What is the probability that more than 3 aircrafts arrive within an hour?
(b)
Consider 15 consecutive and disjoint one hour intervals. What is the probability that in none of these
intervals we have more than 3 aircraft arrivals?
(c)
What is the probability that exactly three aircrafts arrive within 2 hours?
(d)
What is the length of the interval, such that probability of having no arrival within this interval equals
0.1?
(e)
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 Fall '09
 mohammadomar
 Normal Distribution, Variance, Probability theory, probability density function, Cumulative distribution function

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