Consider a digital transmission channel. LetX be a random variable representing the number of bits transmitted until the first error occurs, assuming that the transmissions are independent events. LetY be an Exponential random variable representing the time, in hours, until the first error occurs. The variance ofX is 2 and the expected value ofY is 3 hours.

(a) What is the probability that the second bit is in error?

(b) What is the probability that the error will occur in the first 28 minutes?

(c) LetZ=1.4Y3.5X be an indicator used by managers of the transmission channel to evaluate its performance. FindE[Z] andV[Z]

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