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6.) A channel can be visualized as one that transports characters (comprising of only lower case letters of English alphabet) from the transmitter to the receiver. It makes an error by changing one character to another. Let X and Y be the random variables that represent the input and output of this channel respectively. Let the input symbols be equally likely; and the output symbols depend upon the input according to the channel transition probabilities.

a) Find the average mutual information I(X:Y) when

i) every character at the receiver end has equally likely chances of occurrence.
ii) every transmitted character has equally likely chances of being changed to any other character at the receiver end and every other character (different from the character transmitted) at the receiver end has equally likely chances of occurrence

b) What is its channel capacity?

Q2.)b) A radar unit consists of two primary components: a power supply and a transceiver. The power supply has a constant failure rate of 0.0031 failures per operating hour and takes an average of 5 hrs. (mean) to repair (constant repair rate). The transceiver fails an average (mean) of every 100 operating hours (constant failure rate) and takes 3 hrs. to repair(constant repair rate). What is the point availability of the radar unit after 10 hrs. of use? How much does this differ from the steady state availability? If two radar units are operating in parallel (high-level active redundancy), what are the point, interval (after 10 hrs.), and steady-state availability?

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