14.1 Mobile telephones perform handoffs as they move from cell to cell. Duringa

Question

14.1 Mobile telephones perform handoffs as they move from cell to cell. Duringa call, a telephone either performs zero hand- offs (Ho), one handoff (Hi), or more than one handoff (H2). In addition, each call is either long (L), if it lasts more than three minutes, or brief (B). The following table describes the probabilities of the possible types of calls. 0.1 0.1 0.2 B 0.4 0.1 0.1 (a) What is the probability that a brief call (b) What is the probability that a call with (c) What is the probability that a long call will have no handoffs? one handoff will be long? will have one or more handoffs?

Explanation / Answer

Answer to the question is as follows:

a. P( brief call has no handsoffs)

= P( B and H0|B)

= .4/(.4+.1+.1)

= .6667

b. P( H1 and L given it is Long)

= P( H1 and L | L)

= .1/.1+.1

= .50

c. P(L and 1 or more than 1 given its long call)

= (P(L and H1)+P(L and H2))/P(L)

= (.1+.2)/(.1+.1+.2)

= .75

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