Question: Hi, I need some help with this. Consider a digital transmission channel. Let X be a random variable representing the number of bits transmitted until

Hi, I need some help with this.

Consider a digital transmission channel. Let X be a random variable representing the number of bits transmitted until the first error occurs, assuming that the transmissions are independent events. Let Y be an Exponential random variable representing the tine, in hours, until the first error occurs. The variance of X is 5/16 and the expected value of Y is 3 hours.

a) What is the probability that the fourth bit is in error?

b) What is the probability that the error will occur in the first 37 minutes.

c) Let Z = 1.2Y - 4.2X be an indicator used by managers of the transmission channel to evaluate its performance. Find E[Z] and V[Z].

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