ELL727 weekly quiz-9

RV X has mean = 2 and variance = 4, and Y = aX + b. If Y has zero mean and unit variance, then

• a = 2, b = -4

• a = -1, b = 1/2

• a = 1/2, b = -1

• a = -1, b = 2

Θ is a RV uniformly distributed over [0, 2π]. If X = cos Θ and Y = sin Θ, then X and Y are

• Independent and uncorrelated

• Uncorrelated but dependent

• Independent but correlated

• Dependent and correlated

A packet of 100 bits is sent over a noisy channel with bit-flip probability of 1%. The probability of more than 5 bits in the packet received in error can be estimated as

• Q(2)

• Q(2.5)

• Q(4)

• Q(5)

Consider the random process X(t) = A cos(ωt), where ω is a constant and A is a RV uniformly distributed over the interval [-1,1]. Is X(t) a wide-sense-stationary (WSS) process?

• Yes

• No

Consider the random process X(t) = A cos(ωt+θ), where ω and A are constants and θ is a RV uniformly distributed over the interval [-π,π]. Is X(t) an ergodic WSS process?

• Yes

• No