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Poisson & Normal Probabilities - Contingency Tables

See attached file for format and formulas.

Q4: 4 (+) Given the following contingency table:
B B'
A 10 30
A' 25 35
Find the following:
a) A | B
b) A' | B'
c) A | B'

Q4: 5 The manager of a large computer network has developed the following probability distribution of the number of interruptions per day:
Interruptions (X) P(X)
0 0.32
1 0.35
2 0.18
3 0.08
4 0.04
5 0.02
6 0.01
a. Compute the expected number of interruptions per day

Q4: 5 (+) Two investments, X and Y, have the following characteristics:
E(X) = $50, E(Y) = $100, s2X = $9,000, s 2y = $15,000, and s 2XY = $7,500.
If the weight of portfolio assets assigned to investment X is 0.4, compute the
a. portfolio expected return

s2x $9,000
s2y $15,000
s2xy $7,500
E(X) $50
E(Y) $100
w(x) 0.4
b. portfolio risk

Q4: 5 (+) Assume a Poisson distribution.
a. If lamda = 2, find P( X >= 2 ) l = 2
X = 2

Q4: 6 Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1,
as in Table E.2), what is the probability that:
a. Z is less than 1.57
b. Z is greater than 1.84
c. Z is between 1.57 and 1.84

Q4: 6 (+) Given a normal distribution with mean = 100 and standard deviation = 10, what is
a. P( X > 75 ) ? m = 100
b. P( X < 70 ) ? s = 10

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Solution Summary

The solution provides step by step method for the calculation of Poisson and Normal probabilities. Formula for the calculation and Interpretations of the results are also included.

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