Calculate probability that there is at least one computer up

Reference no: EM131811803

Question: Suppose that in a network of 3 computers, at a given time the event that the kth computer is down has overall probability pk, k = 1, 2, 3,, Calculate the probability that at this time there is at least one computer up:

a) Assuming the computers are up or down independently of each other:

b) Assuming that there is probability p of power failure, in which case all the computers are down, but given that there is no power failure the computers are up or down independently of each other.

c) A fair six-sided die has:

the 1 spot face opposite the 6 spot face:

the 2 spot face opposite the 5 spot face:

the 3 spot face opposite the 4 spot face.

Suppose the die is rolled once. Let X be the number of spots showing on top, Y the number of spots showing on one of its side faces, say the leftmost face from a particular point of view.

a) Display the joint probability distribution of X and Y in a suitable table

b) Are X and Y independent?

c) Find Cov(X, Y).

d) Find Vαr (X + Y).

Reference no: EM131811803

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