Mobile telephones perform handoffs as they move from cell to cell. During a call

Question

Mobile telephones perform handoffs as they move from cell to cell. During a call, a telephone either performs zero hand- offs (H0), one handoff (H1), 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. (a) What is the probability that a brief call will have no handoffs? (b) What is the probability that a call with one handoff will be long? (c) What is the probability that a long call will have one or more handoffs?

Explanation / Answer

Ans:

P(L)=0.4,P(B)=0.6,

P(H0)=0.5,P(H1)=0.2,P(H2)=0.3

a)Probability that a brief call will have no handoffs=P(H0/B)

=P(H0 and B)/P(B)

=0.4/0.6=0.67

b)Probability that a call with one handoff will be long=P(L/H1)

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

=0.1/0.2=0.5

c)Probability that a long call will have one or more handoffs=P(H1 or H2/L)

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

=(0.1+0.2)/0.4

=0.3/0.4

=0.75

H0 H1 H2 Marginal pdf L 0.1 0.1 0.2 0.4 B 0.4 0.1 0.1 0.6 Marginal pdf 0.5 0.2 0.3 1

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