Let Y1< Y2< Y3< Y4< Y5 be the order statistics of n=5 independent observations from the...
Let Y1< Y2< Y3< Y4< Y5 be the order statistics of n=5 independent observations from the exponential distribution with mean= 1. determine P(Y1>1) and find the pdf of Y5
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Let Y1< Y2< Y3< Y4< Y5 be the order
statistics of n=5 independent observations from the...
15. (30 points) Let Y1 < Y2 < Y3 < Y4 be the order statistics of a random sample of size n = 4 fr...
15. (30 points) Let Y1 < Y2 < Y3 < Y4 be the order statistics of a random sample of size n = 4 from a distribution with p.d.f.f(x) 2x, 0 < x < 1, zero elsewhere. Evaluate E[Yalyj]. [Hint: First find the joint p.d.f. of Y3 and Y4, and then find the conditional p.d.f. of Y4 given Y3 y3]
15. (30 points) Let Y1
Let Y1<Y2<...<Yn be the order statistics of a random sample of size n from the distribution...
Let Y1<Y2<...<Yn be the
order statistics of a random sample of size n from the distribution
having p.d.f f(x) = e-y , 0<y<, zero elsewhere. Answer the following
questions.
(a) decide whether Z1 = Y2
and Z2=Y4-Y2 are
stochastically independent or not. (hint. first find the joint
p.d.f. of Y2 and Y4)
(b) show that
Z1 = nY1, Z2=
(n-1)(Y2-Y1),
Z3=(n-2)(Y3-Y2), ....,
Zn=Yn-Yn-1
are stocahstically
independent and that each Zi has the exponential
distribution.(hint use change of variable technique)
Let Y1 < Y2 < : : : < Y9 be the order statistics of 9...
Let Y1 < Y2 < : : : < Y9 be the order statistics of 9 independent draws from an exponential distribution that has a mean of 2. (1) Find the PDF of Y2. (2) Compute P[Y9 < 1].
From 6.3-3. Let Y1 < Y2 < . . . < Y9 be the order statistics...
From 6.3-3. Let Y1 < Y2 < . . . < Y9 be the order
statistics of 9 independent draws from an exponential distribution
that has a mean of 2.
(1) Find the PDF of Y2.
(2) Compute P[Y9 < 1].
From 6.3-3. Let Yǐ < ½ < . . . < y) be the order statistis of 9 independent draws from an exponential distribution that has a mean of 2. (1) Find the PDF of Y2 2) Compute PY,1
. Let Y1 < Y2 < · · · < Yn be the order statistics of...
. Let Y1 < Y2 < · · · < Yn be the order statistics of a random sample of size n from an exponential distribution with parameter θ = 1. (a) Find the pdf of Yr. (b) Find the pdf of U = e −Yr .
Let Y1, Y2, …, Y4 be a random sample from a normal distribution with mean 10...
Let Y1, Y2, …, Y4 be a random sample from a normal distribution with mean 10 years and standard deviation 2.5 years. Find the following probabilities. A. P(Y4 > 14 years) B. P(Y1 + Y2 + Y3 + Y4 < 36 years) C. P{(Y1 < 9 years) and (Y2 < 9 years) and (Y3 < 9 years) and (Y4 < 9 years)} Note: B and C are asking different questions. D. Find E(Y1 +...
Suppose Y1, Y2, Y3, Y4, Y5 is a random sample from a gamma distribution where the...
Suppose Y1, Y2, Y3, Y4, Y5 is a random sample from a gamma
distribution where the shape parameter is known to be 2
and the scale parameter is unknown.
a) Show that
is a pivotal quantity.
b) Show that
is a pivotal quantity.
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From 6.3-3. Let Yi < Y2 < < Yg be the order statistics of 9 independent...
From 6.3-3. Let Yi < Y2 < < Yg be the order statistics of 9 independent draws from an exponential distribution that has a mean of 2. (1) Find the PDF of Y2 (2) Compute PIY9 < 1
Let Y1, Y2, and Y3 be independent, N(0, 1)-distributed random variables, and set X1 = Y1...
Let Y1, Y2, and Y3 be independent, N(0, 1)-distributed random variables, and set X1 = Y1 − Y3, X2 = 2Y1 + Y2 − 2Y3, X3 = −2Y1 + 3Y3.Determine the conditional distribution of X2 given that X1 + X3 = x.
Let Y1, Y2, . . . , Yn be independent random variables with Exponential distribution with...
Let Y1, Y2, . . . , Yn be independent random variables with Exponential distribution with mean β. Let Y(n) = max(Y1,Y2,...,Yn) and Y(1) = min(Y1,Y2,...,Yn). Find the probability P(Y(1) > y1,Y(n) < yn).
15. (30 points) Let Y1 < Y2 < Y3 < Y4 be the order statistics of a random sample of size n = 4 from a distribution with p.d.f.f(x) 2x, 0 < x < 1, zero elsewhere. Evaluate E[Yalyj]. [Hint: First find the joint p.d.f. of Y3 and Y4, and then find the conditional p.d.f. of Y4 given Y3 y3]
15. (30 points) Let Y1
Let Y1<Y2<...<Yn be the
order statistics of a random sample of size n from the distribution
having p.d.f f(x) = e-y , 0<y<, zero elsewhere. Answer the following
questions.
(a) decide whether Z1 = Y2
and Z2=Y4-Y2 are
stochastically independent or not. (hint. first find the joint
p.d.f. of Y2 and Y4)
(b) show that
Z1 = nY1, Z2=
(n-1)(Y2-Y1),
Z3=(n-2)(Y3-Y2), ....,
Zn=Yn-Yn-1
are stocahstically
independent and that each Zi has the exponential
distribution.(hint use change of variable technique)
From 6.3-3. Let Y1 < Y2 < . . . < Y9 be the order
statistics of 9 independent draws from an exponential distribution
that has a mean of 2.
(1) Find the PDF of Y2.
(2) Compute P[Y9 < 1].
From 6.3-3. Let Yǐ < ½ < . . . < y) be the order statistis of 9 independent draws from an exponential distribution that has a mean of 2. (1) Find the PDF of Y2 2) Compute PY,1
Suppose Y1, Y2, Y3, Y4, Y5 is a random sample from a gamma
distribution where the shape parameter is known to be 2
and the scale parameter is unknown.
a) Show that
is a pivotal quantity.
b) Show that
is a pivotal quantity.
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
From 6.3-3. Let Yi < Y2 < < Yg be the order statistics of 9 independent draws from an exponential distribution that has a mean of 2. (1) Find the PDF of Y2 (2) Compute PIY9 < 1
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