15.34 Suppose a cellular telephone is equally likely to make zero handoffs (Ho),

Question

15.34 Suppose a cellular telephone is equally likely to make zero handoffs (Ho), one handoff (H), or more than one hand- off (H2). Also, a caller is either on foot (F) with probability 5/12 or in a vehicle (V) (a) Given the preceding information, find ility that dis- osis est dis- the GE three ways to fill in the following prob- ability table: (b) Suppose we also learn that 1/4 of all callers are on foot making calls with no handoffs and that 1/6 of all callers are vehicle users making calls with a single handoff. Given these additional facts find all possible ways to fill in the table of probabilities. t a ity

Explanation / Answer

It is given to us that a cellular telephone is equally likely to make zero handoffs H0, one handoff H1 and more than one handoff H2. So, the probability of each of these events happening is 1/3.

A caller is either on foot(F) with probability 5/12 or in a vehicle with probability(V)

*[the probability of which will become 1-5/12 = 7/12]

(a) the three ways of filling the table could be:

(i) When we consider the two events to be independent of each other so the probability becomes the product of the two probabilities.

(ii) When we consider that the probability of handoffs does not depend on the probability of the caller being on foot or in a vehicle. So, there are total 6 possible events (example the caller is on foot and cellular telephone makes zero handoffs, the caller is on vehicle and the cellular telephone makes more than one handoffs)

(iii) When we consider that the probability of making zero handoffs, one handoffs or more than one handoffs is dependent on the fact whether the caller was on foot or was in a vehicle. In this case we will have to make use of conditional probabilities such as probability of the cellular telephone making Zero handouts given that the caller was on foot i.e. P(H0|F)

(b) We are given in the question P(H0F) = 1/4 and P(H1V) = 1/6. We also know that the probability of zero handoffs, one handoff and more than one handoff has to be equally likely and the probability of the caller being on foot and in a vehicle is 5/12 and 7/12 respectively. Using these information we can fill the above table as:

H0 H1 H2 F 5/36 5/36 5/36 V 7/36 7/36 7/36

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