Calculating the distribution of the random variable Y at the outputThe random variable X at...
Calculating the distribution of the random variable Y at the output
The random variable X at the entrance to the transmission path is sufficient for the following distribution.
The random variable Y at the output of the transmission link only takes three values. The transfer matrix T with is
Answer & Explanation
What you have is a matrix of conditional probabilities, with the entry in row i, column j of T corresponding to . To find the marginal distribution of Y, use the law of total probability:
Note: If p represents a row vector summarizing the probability masses of X, then pT is a row vector summarizing the masses of Y.