Consider a communication source that transmits packets containing digitized speech. After each transmission, the receiver sends a message indicating whether the transmission was successful or unsuccessful. If a transmission is unsuccessful, the packet is re-sent. Suppose a voice packet can be transmitted a maximum of 10 times. Assuming that the results of successive transmissions are independent of one another and that the probability of any particular transmission being successful is p, determine the probability mass function of the rv X = the number of times a packet is transmitted. Then obtain an expression for the expected number of times a packet is transmitted.

Answer Step 1 of 2 Let x be the no. of times the packet is transmitted According to the given data it is a geometric distribution The pmf of geometric distribution is P(X=x)=(1-p) p; x=1,2,3……,10