5 In electrical engineering, the unwanted "noise" on current signals is often modelled by a Normal distribution. Suppose that the noise in a particular current signal has a constant mean of 0.9V. Furthermore if two noise instances, X and Y are sampled 7 seconds apart they have a Bivariate Normal distribution, with Cov(X,Y)=0.04e-T/10 Let X be the noise at time 3 seconds and let Y be the noise at time 8 seconds, so that 7 = 5. a Calculate Cov(X,Y) b Calculate ? and g?. Hint: Var(X) = Cov(X.X)

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5 In electrical engineering, the unwanted "noise" on current signals is
often modelled by a Normal distribution. Suppose that the noise in a
particular current signal has a constant mean of 0.9V. Furthermore if
two noise instances, X and Y are sampled 7 seconds apart they have
a Bivariate Normal distribution, with Cov(X,Y)= 0.04e-T/10
Let X be the noise at time 3 seconds and let y be the noise at time 8
seconds, so that 7 = 5.
a Calculate Cov(X,Y)
b Calculate of and o. Hint: Var(X) = Cov(X, X)
e Calculate px,y
d Calculate the probability that a greater noise is observed at time
3 seconds than at time 8 seconds.
e If the noise at time 3 seconds is 1V, state the distribution and
parameters for the distribution of Y|X=1
Transcribed Image Text:5 In electrical engineering, the unwanted "noise" on current signals is often modelled by a Normal distribution. Suppose that the noise in a particular current signal has a constant mean of 0.9V. Furthermore if two noise instances, X and Y are sampled 7 seconds apart they have a Bivariate Normal distribution, with Cov(X,Y)= 0.04e-T/10 Let X be the noise at time 3 seconds and let y be the noise at time 8 seconds, so that 7 = 5. a Calculate Cov(X,Y) b Calculate of and o. Hint: Var(X) = Cov(X, X) e Calculate px,y d Calculate the probability that a greater noise is observed at time 3 seconds than at time 8 seconds. e If the noise at time 3 seconds is 1V, state the distribution and parameters for the distribution of Y|X=1
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