Question

In: Statistics and Probability

Expect that a connection has a lossy tendency of 10% and that packet losses are independent....

Expect that a connection has a lossy tendency of 10% and that packet losses are independent. Assume that when a packet gets lost, this is detectable and the packet is re-transmitted until the point that it is accurately received. What is the probability that it would be transmitted precisely one, two, and three times?

Expert Solution

Given,

Probability that a packet gets lost : p = 10/100 =0.1

Probability that a packet is received accurately : q = 1-p = 1-0.9

probability that it would be transmitted precisely one, two, and three times

Probability that it would be transmitted precisely one time

=Probability that First time itself that the packet is received accurately

= Probability that the packet is received accurately : q = 0.9

Probability that it would be transmitted precisely one time = 0.9

Probability that it would be transmitted precisely second time

= Probability that First time the packet is lost and Second time the packet is received accurately

=Probability that the packet is lost x Probability that the packet is is received accurately

= pq = 0.1 x 0.9 = 0.09

Probability that it would be transmitted precisely second time =0.09

Probability that it would be transmitted precisely second time = 0.09

Probability that it would be transmitted precisely third time =

Probability that First time the packet is lost and Second time the packet is lost and Third time the packet is received accurately

=Probability that the packet is lost x Probability that the packet is lost x Probability that the packet is received accurately

p x p x q = 0.1 x 0.1 x 0.9 = 0.009

Probability that it would be transmitted precisely third time = 0.009

orchestra answered 2 years ago

In Hilbert's Axioms, all of the axioms of connection are independent of each other

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