b) Suppose that 10% of the values of a normally distributed random variable X are below 50, and 5% of the values are above 100. Find the mean and variance of X.

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a) A 2-bit binary sequence is transmitted over a noisy communication channel. The noise corrupts the signal
in the sense that a transmitted digit transmitted can be flipped with probability 0.15. It has been observed
that, across a large number of transmitted signals, the Os and 1s are transmitted in the ratio 1:3. Given that
the sequence 00 is received, calculate the probability that this sequence was transmitted.
b) Suppose that 10% of the values of a normally distributed random variable X are below 50, and 5% of
the values are above 100. Find the mean and variance of X.
Transcribed Image Text:a) A 2-bit binary sequence is transmitted over a noisy communication channel. The noise corrupts the signal in the sense that a transmitted digit transmitted can be flipped with probability 0.15. It has been observed that, across a large number of transmitted signals, the Os and 1s are transmitted in the ratio 1:3. Given that the sequence 00 is received, calculate the probability that this sequence was transmitted. b) Suppose that 10% of the values of a normally distributed random variable X are below 50, and 5% of the values are above 100. Find the mean and variance of X.
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