Homework Answers
We will use the central limit theorem which states that the mean of a sufficiently large sample is approximately normally distributed the parameters of which will be specified below.
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7. (1 point) Let X be the mean of a random sample of size 36 from...
5.6 6. (1 point) Let X be the weight of a newborm blue whale. It is...
5.6 6. (1 point) Let X be the weight of a newborm blue whale. It is known that the population mean weight is 5,000 pounds with a population standard deviation of 1,000 pounds. If a random sample of 25 newborn blue whales were weighed, and their sample mean X were calculated, find P(X 2 5,100). 7. (1 point) Let X be the mean of a random sample of size 36 from the uniform distribution U (7,15) Find P(11.3 < X...
Let X be the mean of a random sample of size n = 75 from the...
Let X be the mean of a random sample of size n = 75 from the uniform distribution on the interval (0,4), .e 0, otherwise. Approximate the probability P(1.84 < X 〈 2.16).
Let X be the mean of a random sample of size n = 75 from the...
Let X be the mean of a random sample of size n = 75 from the uniform distribution on the interval (0,4), .e 0, otherwise. Approximate the probability P(1.84 < X 〈 2.16).
(1 point) Let X1 and X2 be a random sample of size n= 2 from the...
(1 point) Let X1 and X2 be a random sample of size n= 2 from the exponential distribution with p.d.f. f(x) = 4e - 4x 0 < x < 0. Find the following: a) P(0.5 < X1 < 1.1,0.3 < X2 < 1.7) = b) E(X1(X2 – 0.5)2) =
Let X and Y be two continuous random variables having the joint probability density 24xy, for...
Let X and Y be two continuous random variables having the joint probability density 24xy, for 0 < x < 1,0<p<1.0<x+y<1 0, elsewhere Find the joint probability density of Z X + Y and W-2Y.
1. Let X1, ..., Xn be random sample from a distribution with mean y and variance...
1. Let X1, ..., Xn be random sample from a distribution with mean y and variance o2 < 0. Prove that E[S] So, where S denotes sample standard deviation. 10 points
f a random sample X,X, X, from the 2. Let Y, < Y.< Y, be the...
f a random sample X,X, X, from the 2. Let Y, < Y.< Y, be the order statistics o exponential distribution with mean β. Let (i) Are the random variables U,V,W independent? (ii) What is the distribution of each of U,V and W.
2.Let Xj,X,, Xj, X4, Xj be a random sample of size n-5 from a Poisson distribution...
2.Let Xj,X,, Xj, X4, Xj be a random sample of size n-5 from a Poisson distribution with mean ?. Consider the test Ho : ?-2.6 vs. H 1 : ? < 2.6. a)Find the best rejection region with the significance level a closest to 0.10 b) Find the power of the test from part (a) at ?= 2.0 and at ?=1.4. c) Suppose x1-1, x2-2, x3 -0, x4-1, x5-2. Find the p-value of the test.
6. Let X be a normal random variable with mean u = 10. What is the...
6. Let X be a normal random variable with mean u = 10. What is the standard deviation o if it is known that p (IX – 101 <>) =
A random sample of size n = 2 is taken from the p.d.f f(x) = {1...
A random sample of size n = 2 is taken from the p.d.f
f(x) = {1 for 0 ≤ x ≤ 1 and 0 otherwise.
Find P(X-bar ≥ 0.9)
3. A random sample of size n = 2 is taken from the p.d.f 1 for 0 < x < 1 f(30 0 otherwise. Find P(X > 0.9)
5.6 6. (1 point) Let X be the weight of a newborm blue whale. It is known that the population mean weight is 5,000 pounds with a population standard deviation of 1,000 pounds. If a random sample of 25 newborn blue whales were weighed, and their sample mean X were calculated, find P(X 2 5,100). 7. (1 point) Let X be the mean of a random sample of size 36 from the uniform distribution U (7,15) Find P(11.3 < X...
Let X be the mean of a random sample of size n = 75 from the uniform distribution on the interval (0,4), .e 0, otherwise. Approximate the probability P(1.84 < X 〈 2.16).
Let X be the mean of a random sample of size n = 75 from the uniform distribution on the interval (0,4), .e 0, otherwise. Approximate the probability P(1.84 < X 〈 2.16).
(1 point) Let X1 and X2 be a random sample of size n= 2 from the exponential distribution with p.d.f. f(x) = 4e - 4x 0 < x < 0. Find the following: a) P(0.5 < X1 < 1.1,0.3 < X2 < 1.7) = b) E(X1(X2 – 0.5)2) =
Let X and Y be two continuous random variables having the joint probability density 24xy, for 0 < x < 1,0<p<1.0<x+y<1 0, elsewhere Find the joint probability density of Z X + Y and W-2Y.
1. Let X1, ..., Xn be random sample from a distribution with mean y and variance o2 < 0. Prove that E[S] So, where S denotes sample standard deviation. 10 points
f a random sample X,X, X, from the 2. Let Y, < Y.< Y, be the order statistics o exponential distribution with mean β. Let (i) Are the random variables U,V,W independent? (ii) What is the distribution of each of U,V and W.
2.Let Xj,X,, Xj, X4, Xj be a random sample of size n-5 from a Poisson distribution with mean ?. Consider the test Ho : ?-2.6 vs. H 1 : ? < 2.6. a)Find the best rejection region with the significance level a closest to 0.10 b) Find the power of the test from part (a) at ?= 2.0 and at ?=1.4. c) Suppose x1-1, x2-2, x3 -0, x4-1, x5-2. Find the p-value of the test.
6. Let X be a normal random variable with mean u = 10. What is the standard deviation o if it is known that p (IX – 101 <>) =
A random sample of size n = 2 is taken from the p.d.f
f(x) = {1 for 0 ≤ x ≤ 1 and 0 otherwise.
Find P(X-bar ≥ 0.9)
3. A random sample of size n = 2 is taken from the p.d.f 1 for 0 < x < 1 f(30 0 otherwise. Find P(X > 0.9)
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