ELL727 weekly quiz-8

A noisy binary symmetric channel has 20% probability of causing a bit-flip during transmission. A random binary message containing 40% '0's is sent through this channel. If a bit is received as '1', the probability that it was originally sent as '0' is

• 1/5

• 1/6

• 1/7

• 1/8

Which of the following is an invalid CDF (Cumulative Density Function) F_X(x)? The sample space range is x ∊ [0, π/2]

• sin x

• sin^1/2x

• sin²x

• sin 2x

Consider the probability density function (PDF) p_X(x) = ke^-2x, where the sample space range is x ∊ [0, ∞). The value of k is

• 2

• 1

• 1/2

• 2/e

The mean time-to-failure for a type of electronic component is found to be 5 years, with a standard deviation of 2 years. Modeling the time-to-failure as a Gaussian random variable, the chance of a newly deployed component working for at least the next 10 years is

• Q (2) ~ 2.3%

• Q (0.5) ~ 31%

• Q (2.5) ~ 0.6%

• Q (1.6) ~ 5.5%

The mean value of a random variable X with PDF p_X(x) = e^-|x|/2 is