Homework Answers
1. [8 points] Suppose Xi... Xn is a random sample from a Pareto distribution with the...
1. [8 points] Suppose Xi... Xn is a random sample from a Pareto distribution with the density If x > 1 otherwise, where ? > 1, Find the method of moments estimator of ?.
show that if ch[k-n], h[k] > = Ži h*[kn] h[k] = Str], then I Herita, 1...
show that if ch[k-n], h[k] > = Ži h*[kn] h[k] = Str], then I Herita, 1 = 1 K:-00 - ICWCTI
2. If X and Y are independent random variables, X has a normal distribution with mean...
2. If X and Y are independent random variables, X has a normal distribution with mean 2 variance 4, and Y has a chi-square distribution with 9 degrees of freedom, then find u such that P(X > 2+11,7)=0.01.
2) (3 pts) Use mathematical induction to show that when n is an exact power of...
2) (3 pts) Use mathematical induction to show that when n is an exact power of 2, the solution of the recurrence 2, ifn=2 T(n) =127G)+n, ifn=2.for k > 1 ISI(72) = n lg n.
3. The following utility function is known as CES (constant elasticity of substi- tution) function where...
3. The following utility function is known as CES (constant elasticity of substi- tution) function where α > 0 β > 0 (a) Is this function homothetic? (b) How does the MRS,y depend on the ratio x/y? Specifically, show that the MRSy is strictly decreasing in the ratio x/y for all values δ < 1, increasing in the ratio x/y for all values δ > 1 and constant for δ 1. (c) Show that if x = y, the MRS...
1. Suppose the random variable as a uniform distribution on [-k,k] a) Construct the pdf X....
1. Suppose the random variable as a uniform distribution on [-k,k] a) Construct the pdf X. b) Calculate P(X > 2X > 1) in terms of 'k c) Calculate 'K if P(-2 < X < 2) =
(b) Find an example of an open set G in a metric space X and a...
(b) Find an example of an open set G in a metric space X and a closed subset F of G such that there is no δ > 0 with {x : dist(x, F) < δ} C G
The random variable Z has a Normal distribution with mean 0 and variance 1. Show that...
The random variable Z has a Normal distribution with mean 0 and variance 1. Show that the expectation of Z given that a < Z < b is o(a) – °(6) 0(b) – (a)' where Ø denotes the cumulative distribution function for Z.
If correct i will thumbs up. Show all steps please 3) 900n ww USE THE MESH...
If correct i will thumbs up. Show all steps please
3) 900n ww USE THE MESH /23v 1.2K 720 s2 CURRENT MIE1>0 SHow woRK No
A Pareto distribution is often used in economics to explain a distribution of wealth. Let a...
A Pareto distribution is often used in economics to explain a
distribution of wealth. Let a random variable X have a Pareto
distribution with parameter θ so that its probability distribution
function is
for
and 0 otherwise. The parameters and
are
known and fixed; is a constant to
be determined.
a) Assuming that
find the expected value and variance of ?
b) Show that for 3 ≥ θ > 2 the Pareto distribution has a
finite mean but infinite variance,...
1. [8 points] Suppose Xi... Xn is a random sample from a Pareto distribution with the density If x > 1 otherwise, where ? > 1, Find the method of moments estimator of ?.
show that if ch[k-n], h[k] > = Ži h*[kn] h[k] = Str], then I Herita, 1 = 1 K:-00 - ICWCTI
2. If X and Y are independent random variables, X has a normal distribution with mean 2 variance 4, and Y has a chi-square distribution with 9 degrees of freedom, then find u such that P(X > 2+11,7)=0.01.
2) (3 pts) Use mathematical induction to show that when n is an exact power of 2, the solution of the recurrence 2, ifn=2 T(n) =127G)+n, ifn=2.for k > 1 ISI(72) = n lg n.
3. The following utility function is known as CES (constant elasticity of substi- tution) function where α > 0 β > 0 (a) Is this function homothetic? (b) How does the MRS,y depend on the ratio x/y? Specifically, show that the MRSy is strictly decreasing in the ratio x/y for all values δ < 1, increasing in the ratio x/y for all values δ > 1 and constant for δ 1. (c) Show that if x = y, the MRS...
1. Suppose the random variable as a uniform distribution on [-k,k] a) Construct the pdf X. b) Calculate P(X > 2X > 1) in terms of 'k c) Calculate 'K if P(-2 < X < 2) =
(b) Find an example of an open set G in a metric space X and a closed subset F of G such that there is no δ > 0 with {x : dist(x, F) < δ} C G
The random variable Z has a Normal distribution with mean 0 and variance 1. Show that the expectation of Z given that a < Z < b is o(a) – °(6) 0(b) – (a)' where Ø denotes the cumulative distribution function for Z.
If correct i will thumbs up. Show all steps please
3) 900n ww USE THE MESH /23v 1.2K 720 s2 CURRENT MIE1>0 SHow woRK No
A Pareto distribution is often used in economics to explain a
distribution of wealth. Let a random variable X have a Pareto
distribution with parameter θ so that its probability distribution
function is
for
and 0 otherwise. The parameters and
are
known and fixed; is a constant to
be determined.
a) Assuming that
find the expected value and variance of ?
b) Show that for 3 ≥ θ > 2 the Pareto distribution has a
finite mean but infinite variance,...
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