Write A function Markov that take ?, ? and ? as inputs and return the upper bounds for ?(?≥?⋅??) given by the below Markov inequalities as output.
For the binomial distribution
with mean
and variance
,
we would like to upper bound the probability
for
.
Example:
Markov(100.,0.2,1.5)
Output:
0.6666666666666666
Which of the following is the correct output for Markov(200.,0.3,1.1)?
A. 0.909
B 0.558
C. 0.986
D. 0872
Write A function Markov that take ?, ? and ? as inputs and return the upper...
Suppose that
is a bounded function with following Lower and Upper
Integrals:
and
a) Prove that for every
, there exists a partition
of
such that the difference between the upper and lower sums
satisfies
.
b) Furthermore, does there have to be a subdivision such that
. Either prove it or find a counterexample and show to the
contrary.
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Negative binomial probability function:
is the mean
is the dispersion
parameter
Let there be two groups with numbers and means of
1) Write down the log-likelihood for the full model
2) Calculate the likelihood equations and find the general form
of the MLE for and
3) Write down the likelihood function in the reduced model (ie.
assuming )
and derive the MLE for in general
terms
4) Using the above answers only, give the MLE and standard error
for where...
(6) The sequence of random variable
are independent of each other and they follow the normal
distribution
.
However, the actual value of were not
observed, instead we only observed if each is either
greater than or
equal to 0, or less than 0.
And you can use the fact that there is the inverse function
that is continuous.
Answer the following questions.
Find
the maximum likelihood estimator
of .
When
, show
, where
represents conversion of probability....
Question
If
a) Find the angle between
b) Find a scalar projection and a vector projection of
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Let f(x)=
if
,
if
if
a) What is the fomain of f(x)? Write in interval notation.
b) Determine the y-intercept of the function, if any. Make sure
to justify your answer.
c) Determine the x-intercepts of the function, if any. Justify
your answer.
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Let X be a banach space such that X= C([a,b]) where - ab+ with the sup
norm. Let x and f X. Show
that the non linear integral equation
u(x) = (sin
u(y) dy + f(x) ) has a solution u X. (the integral is
from a to b).
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sin 0, cos 0
Name the quadrant in which the angle lies
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Let be the distribution
function defined by
Let be the
Lebesgue-Stieltjes measure asociated to .
Determine the measurements of the fpllowing sets:
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Prove that for every positive real (important: is not
necessarily an integer), that
.
Hint: For every , the function
is
strictly growing.
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Let
be a simple random sample of a random variable X with density
function
, .
Given the statistic :
Calculate a statistic ( function of ) such that its espected
value is equal to
.
Thank you for your explanations
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