A juicer works for T amount of time before it breaks, where T
follows the exponential distribution with rate
= 3. After sales service examines the juicer at times distributed
according to a Poisson process with rate
= 2; if the juicer is found to be not working then it is
immediately substituted.
1) Find the probability that a juicer is examined at least 2 times before it stops working.
2) Find the expected time between replacements of juicers.
A juicer works for T amount of time before it breaks, where T follows the exponential...
Every element shown in the circuit works independently of each
other. The working life length of each element has an exponential
distribution with parameter . That
is
. Find the density function of the working life length of the
entire system T.
We were unable to transcribe this imageT, ~ exp(%) 3 4 2
Every element shown in the circuit works independently of each
other. The working life length of each element has an exponential
distribution with parameter . That
is
. Find the density function of the working life length of the
entire system T.
We were unable to transcribe this imageT, ~ exp(%) 3 4 2
Let X1, X2, X3 ∼(iid) Exponential(λ).
(a) Show that T(X1, X2, X3) = X1 + X2 + X3 is a sufficient
statistic for λ.
(b) Find the MVUE for λ.
(c) Show that
is not a sufficient statistic for λ.
(d) Let
=
and find
. Give an argument for why
is not the best estimator of λ.
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The median of a probability distribution is the value that is
exceeded 1/2 of the time.
(a) Find the median of an exponential distribution with mean
.
(b) Find the probability an observation exceeds
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Consider the Solow growth model that we developed in class. Output at time t is given by the production function where A is total factor productivity, Kt is total capital at time t and L is the labour force. Total factor productivity A and labour force L are constant over time. There is no government or foreign trade and where Ct is consumption and It is investment at time t. Every agent saves s share of his income and consumes...
(19) i(t) By using the time-domain technique, find in the electric circuit shown in Figure P.6 when vs(t) is defined by Figure 2.19 We were unable to transcribe this imageWe were unable to transcribe this image
The following circuit consists of linear time invariant
components where R1 = 2,
R2 = 3,
C = 0.25F, and L = 1H. Let vs be the input voltage.
(a) Solve the differential equation that describes
vc(t). Hint: First, find the current
going through the parallel branch of R1–C. Then, write
the Kirchoff's Voltage Law for the main loop.
(b) Find vc(t) given that vs(t) = 2.5 V at
t = 0. Assume that vc(0-) = 1V and
iL(0-) =...
For the following circuit:
At t=0 the voltage drop on the capacitor is and
points s and 1 are connected.
1) Which of the following statement describe what will happen in
the circuit ? (select one)
a. The capacitor will be charged to a final voltage of , with I
being the current in the circuit
b. The capacitor will disconnect the circuit so no current will
exist
c. The voltage will oscillate at an angular frequency of
d. The...
Please help solve this, using the equation
to get through the problem.
Additional information:
where the initial position
, the initial speed
The above differential equation can also be written as:
If
, there is light damping where the solution has the form ( where r
and w are two positive constants)
or
If
there is heavy damping where,
where
and
are two positive constants
If
there is critical damping where,
where r is a positive constant
d'y dy ma...
The magnetic flux can be estimated to be ΦB(t) =
NB(t)A.
The coil is connected to two light bulbs in a series with a
voltage of 6.6v
N=200 turns
A= 0.0314
The magnetic field is uniform over the area
Bo is the maximum value of the magnetic field
2π f=is more compactly written as the angular frequency
1) Use the expression
and the are (expressed in terms of the diameter) to
write out an expression for the (time-dependent) magnetic flux:...