Probability distribution of the number of interruptions

Question

Discuss the following:

Q1: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 ‘

Q2: 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

Q3: 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

E(P)=w(X)E(x)+(1-w(X))E(Y)

s2x $9,000

s2y $15,000

s2xy $7,500

E(X) $50

E(Y) $100

w(x) 0.4

b. portfolio risk

Q4:Assume a Poisson distribution.

a. If lamda = 2, find P( X >= 2 )

Q5: Given a standardized normal distribution (with a mean of 0 and a standard deviattion of 1), 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 ?

Q6: Given a normal distribution with mean = 100 and standard deviation = 10, what is

a. P( X > 75 ) μ= 100

b. P( X < 70 ) σ = 10