Determine the currents through the various branches of the electrical network in the
figure using the Gauss-Jordan elimination operation.
The following stochastic matrix P gives the probabilities for a certain region of
college- and noncollege-educated households having at least one college-educated
child. By college-educated we understand that at least one parent is college educated,
while by noncollege-educated we mean that neither parent is college-educated. If there
are currently 300,000 college-educated households and 750,000 noncollege-educated
households, what is the predicted distribution for two generation hence?
Let the set {v1, v2 , v3} be linearly independent in R3 . Let c be a nonzero scalar.
Prove that the set {v1, v1 + cv2 , v3} are also linearly independent.
Explain the definitions for these terms; (1) a priori, (2) a posteriori, (3) the sample
space of the experiment.
We may model the arrival of telephone calls with a Poisson probability density
function. Suppose that the average rate of calls is 10 per minute, What is the
probability that less than three calls will be received in the first six seconds? In the
first six minutes?
Suppose two random variables are related such that Y = aX2 . Assume that PY( y) is
even about the origin. Show that ρXY = 0 .
A Gaussian random variable with zero mean (μ = 0) and variance σ2 is applied to
a device that has only two possible outputs, zero or one. The output zero occurs when
the input is negative, and the output one occurs when the input is zero or positive.
What is the output probability density function? Rework the problem when μ = 0.5
and σ = 1.
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