# Poisson & Normal Probabilities - Contingency Tables

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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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