Binary bits are transmitted in a digital communication with bit error probability of 0.1, and bit error probability for each transmitted bit is independent each other. Answer the following questions.
(1) Random variable X denotes the number of bit errors when a bit is transmitted. Derive the second central moment of X.
(2) Random variable Y denotes the number of transmitted bits until you find the second bit error. Find the PMF of Y, and find the probability that Y is greater than 3.
(3) Random variable W denotes the number of errors among 100 transmitted bits, and is approximated to a Gaussian random variable with a mean value of 10 and variance of 9. Find out the probability that W is greater than or equal to 4 and less than or equal to 7. (You can represent the answer in terms of Q()).
(4) The event Ai is defined by the event when W=i., find out the number of elements in A3, and determine if all Aisare collectively exhaustive.
(5) If a random variable H is defined by H=20W+19, then find the second central moment of H.
(6) A random variable K is the number of bit errors when 2 bits are transmitted. When L= -K+2, find the PMF of L.