Reference no: EM131084469
In the message transmission problem, Problem 5.3.2, the PMF for the number of transmissions
when message i is received successfully is
Let J3 = K3 - K2, the number of transmissions of message 3; J2 = K2 - K1, the number of transmissions of message 2; and J1 = K1, the number of transmissions of message 1. Derive a formula for PJ(j), the PMF of the number of transmissions of individual messages.
Problem:
A wireless data terminal has three messages waiting for transmission. After sending a message, it expects an acknowledgement from the receiver. When it receives the acknowledgement, it transmits the next message. If the acknowledgement does not arrive, it sends the message again. The probability of successful transmission of a message is p independent of other transmissions. Let K = [K1 K2 K3] be the 3-dimensional random vector in which Ki is the total number of transmissions when message i is received successfully. (K3 is the total number of transmissions used to send all three messages.) Show that
(a) Find the PMF of K.
(b) For each j ∈ {1, 2,..., n - 1}, find the marginal PMF PK1,K2,...,K j(k1, k2,..., kj)
(c) For each i ∈ {1, 2,..., n}, find the marginal PMF PKi(ki).
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: Let J3 = K3 - K2, the number of transmissions of message 3; J2 = K2 - K1, the number of transmissions of message 2; and J1 = K1, the number of transmissions of message 1. Derive a formula for PJ(j), the PMF of the number of transmissions of individ..
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