onitor three consecutive phone calls going through a telephone switching office. Classify each on ice call (v) if someone is speaking or data call (d) if the call is carrying a modem or a fax signal servation is a sequence of letters (each one is either v or d). The outcomes vvv and ddd has prob 2 each and other outcomes have probability 0.1. Count the number of voice calls Nv in the thre u have observed. Consider the four events Nv = 0, Nv = 1, Nv = 2 and Nv = 3. Calculate the foll obabilities. a. P[ {ddv} / Nv = 2] b. P[Nv = 2/ Nv 2 1] C. P[ Nv 21 / Nv = 2 ]
onitor three consecutive phone calls going through a telephone switching office. Classify each on ice call (v) if someone is speaking or data call (d) if the call is carrying a modem or a fax signal servation is a sequence of letters (each one is either v or d). The outcomes vvv and ddd has prob 2 each and other outcomes have probability 0.1. Count the number of voice calls Nv in the thre u have observed. Consider the four events Nv = 0, Nv = 1, Nv = 2 and Nv = 3. Calculate the foll obabilities. a. P[ {ddv} / Nv = 2] b. P[Nv = 2/ Nv 2 1] C. P[ Nv 21 / Nv = 2 ]
Transcribed Image Text:**Title: Probability Calculation in Telephone Switching**
*Objective:*
Monitor three consecutive phone calls going through a telephone switching office. Classify each call as a voice call (v) if someone is speaking, or a data call (d) if the call is carrying a modem or fax signal. Each observation is represented by a sequence of letters (either 'v' or 'd').
*Probabilities:*
- The outcomes 'vvv' and 'ddd' each have a probability of 0.2.
- All other outcomes have a probability of 0.1.
*Instructions:*
Count the number of voice calls, denoted as Nv, in the sequence of three calls. Consider the events where Nv is equal to 0, 1, 2, and 3. Calculate the following probabilities:
a. \( P(\{ddv\} \mid Nv = 2) \)
b. \( P(Nv = 2 \mid Nv \geq 1) \)
c. \( P(Nv \geq 1 \mid Nv = 2) \)
These calculations will help understand the distribution and likelihood of voice versus data calls in a monitored sequence.
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