Homework Answers
There is another form of gamma distribution
here i have assumed the gamma distribution with parameters shape
and rate.
Add Answer to:
Assume the MRI sensor intensity X has a Gamma distribution with u = 12 and a...
7. Assume X gammala, y) and Y-gamma(8,7) are independent. (a) Show that U = X +...
7. Assume X gammala, y) and Y-gamma(8,7) are independent. (a) Show that U = X + Y gamma(a +.). (b) Show that V = X/(X+Y) beta(a. 8). (c) Show that U and V are independent. (d) Show that W = 72 gamma(1/2, 1/2) if Z N (0,1).
Problem 10: 10 points Assume that a random variable (L) follows the exponential distribution with intensity...
Problem 10: 10 points Assume that a random variable (L) follows the exponential distribution with intensity λ-1. Given L-u, a random variable Y has the Poisson distribution with parameter - u. 1. Derive the marginal distribution of Y and evaluate probabilities, PY=n] , for n = 0,1,2, 2. Find the expectation of Y, that is E Y 3. Find the variance of Y, that is Var Y
4. Assume that x has a normal distribution with u = 2.8 and o = 0.33....
4. Assume that x has a normal distribution with u = 2.8 and o = 0.33. Find Plx 22). A. 0.9922 B. 0.6485 C. 0.4523 D. 0.0078 Suppose x has a distribution with u = 54 and o = 4. If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means? A. Yes, the x distribution is normal with mean Hz = 54 and 0 = 1. B. Yes, the...
7. The Gamma distribution is commonly used to model continuous data. The probability density function of...
7. The Gamma distribution is commonly used to model continuous data. The probability density function of a Gamma random variable is f (zlo, β)- a. Find the MGF of a Gamma random variable. b. Use the MGF to find the mean of a Gamma random variable. c. Use the MGF to find the second raw moment of a Gamma random variable. d. Use results (b) and (c) to find the variance of a Gamma random variable. e. Let Xi, í...
This is 'Maple' question. (showing work on Maple) 6. Let X be a Gamma distribution with...
This is 'Maple' question. (showing work on Maple)
6. Let X be a Gamma distribution with mean 8 and variance 32. Let X1, X2, ..., Xn be n independent random variables with the same distribution as X. Let Yn = 21-1X;/n be the sample mean. Sketch the graphs of the pdf of X and the pdf of Yn for n = 3,5. What do you observe? Can you compare Yn to a known distribution when n is large? Elaborate on...
15 marksLet Xi ~ Gamma(k, λ), (a) 5 marks] Show that X2 has a PDF given...
15 marksLet Xi ~ Gamma(k, λ), (a) 5 marks] Show that X2 has a PDF given by 0. (b) [5 marks] Use the conditional mean and variance fornulae given in Theorem 2.40 to find E(X2 and Var(X2), for k> 2. (This means don't derive them directly from the PDF given in part (a). (c) [5 marks] Show that XIX,-x2 ~ Gamma(k +1, λ +12).
2. 12 points Bjorn, a member of ABBA, knows that X (which is the amount an ABBA song brightens or worsens a person's day) has a Normal distribution with a mean of 0... and he's OK with th...
2. 12 points Bjorn, a member of ABBA, knows that X (which is the amount an ABBA song brightens or worsens a person's day) has a Normal distribution with a mean of 0... and he's OK with that. What he wants to learn more about is the precision of X, which is the inverse of the variance. Bjorn thinks that the precision has a Gamma distribution as described below. Help Bjorn out by finding the posterior distribution for the percision....
Please show steps (and formulas) for part b Problem 2. a. X has a normal distribution...
Please show steps (and formulas) for part b
Problem 2. a. X has a normal distribution with mean 5 and variance 25. Y has a normal distribution with mean 3 and variance 16. In addition, X and Y are independent. If W = X+Y, find P(W > 9). b. Random variables U, V, Z are such that E[U] = 1, E[V] =5, E[2] = -3, Var[U] = 1, Var[V] = 4, Var[2] =1, Cov[U,V] =-1,Cov[U, 2] = 2, Cor[V, 2]...
X denote the mean of a random sample of size 25 from a gamma type distribu-...
X denote the mean of a random sample of size 25 from a gamma type distribu- tion with a = 4 and β > 0. Use the Central Limit theorem to find an approximate 0.954 confidence interval for μ, the mean of the gallina distribution. Hint: Use the random variable (X-43)/?7,/432/25. 6. Let Yi < ½ < < }, denote the order statistics of a randon sample of size n from a distribution that has pdf f(z) = 4r3/04, O...
Having troubles with question 2. Please help 2. If X has a Gamma distribution with parameters...
Having troubles with question 2. Please help
2. If X has a Gamma distribution with parameters a and B, then its mgf is given by (a) Obtain expressions for the moment-genérating functions of an exponential random variable and of a chi-square random variable by recognizing that these are special cases of a Gamma distribution and using the mgf given above. (b) Suppose that X1 is a Gamma variable with parameters α1 and β, X2 is a Gamma variable with parameters...
7. Assume X gammala, y) and Y-gamma(8,7) are independent. (a) Show that U = X + Y gamma(a +.). (b) Show that V = X/(X+Y) beta(a. 8). (c) Show that U and V are independent. (d) Show that W = 72 gamma(1/2, 1/2) if Z N (0,1).
Problem 10: 10 points Assume that a random variable (L) follows the exponential distribution with intensity λ-1. Given L-u, a random variable Y has the Poisson distribution with parameter - u. 1. Derive the marginal distribution of Y and evaluate probabilities, PY=n] , for n = 0,1,2, 2. Find the expectation of Y, that is E Y 3. Find the variance of Y, that is Var Y
4. Assume that x has a normal distribution with u = 2.8 and o = 0.33. Find Plx 22). A. 0.9922 B. 0.6485 C. 0.4523 D. 0.0078 Suppose x has a distribution with u = 54 and o = 4. If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means? A. Yes, the x distribution is normal with mean Hz = 54 and 0 = 1. B. Yes, the...
7. The Gamma distribution is commonly used to model continuous data. The probability density function of a Gamma random variable is f (zlo, β)- a. Find the MGF of a Gamma random variable. b. Use the MGF to find the mean of a Gamma random variable. c. Use the MGF to find the second raw moment of a Gamma random variable. d. Use results (b) and (c) to find the variance of a Gamma random variable. e. Let Xi, í...
This is 'Maple' question. (showing work on Maple)
6. Let X be a Gamma distribution with mean 8 and variance 32. Let X1, X2, ..., Xn be n independent random variables with the same distribution as X. Let Yn = 21-1X;/n be the sample mean. Sketch the graphs of the pdf of X and the pdf of Yn for n = 3,5. What do you observe? Can you compare Yn to a known distribution when n is large? Elaborate on...
15 marksLet Xi ~ Gamma(k, λ), (a) 5 marks] Show that X2 has a PDF given by 0. (b) [5 marks] Use the conditional mean and variance fornulae given in Theorem 2.40 to find E(X2 and Var(X2), for k> 2. (This means don't derive them directly from the PDF given in part (a). (c) [5 marks] Show that XIX,-x2 ~ Gamma(k +1, λ +12).
2. 12 points Bjorn, a member of ABBA, knows that X (which is the amount an ABBA song brightens or worsens a person's day) has a Normal distribution with a mean of 0... and he's OK with that. What he wants to learn more about is the precision of X, which is the inverse of the variance. Bjorn thinks that the precision has a Gamma distribution as described below. Help Bjorn out by finding the posterior distribution for the percision....
Please show steps (and formulas) for part b
Problem 2. a. X has a normal distribution with mean 5 and variance 25. Y has a normal distribution with mean 3 and variance 16. In addition, X and Y are independent. If W = X+Y, find P(W > 9). b. Random variables U, V, Z are such that E[U] = 1, E[V] =5, E[2] = -3, Var[U] = 1, Var[V] = 4, Var[2] =1, Cov[U,V] =-1,Cov[U, 2] = 2, Cor[V, 2]...
X denote the mean of a random sample of size 25 from a gamma type distribu- tion with a = 4 and β > 0. Use the Central Limit theorem to find an approximate 0.954 confidence interval for μ, the mean of the gallina distribution. Hint: Use the random variable (X-43)/?7,/432/25. 6. Let Yi < ½ < < }, denote the order statistics of a randon sample of size n from a distribution that has pdf f(z) = 4r3/04, O...
Having troubles with question 2. Please help
2. If X has a Gamma distribution with parameters a and B, then its mgf is given by (a) Obtain expressions for the moment-genérating functions of an exponential random variable and of a chi-square random variable by recognizing that these are special cases of a Gamma distribution and using the mgf given above. (b) Suppose that X1 is a Gamma variable with parameters α1 and β, X2 is a Gamma variable with parameters...
Most questions answered within 3 hours.
-
A 2400-kg airplane pulls two gliders, the first of mass 330 kg
and the second of...
asked 5 minutes ago -
When I have a regression equation such as Y = beta 0 + beta 1 X...
asked 9 minutes ago -
1) Describe how the firm, Google is organized. a. Note the
formal structure (Organizational Charts); also...
asked 16 minutes ago -
Q 1 Give a numerical example of non routine decision,
Determine the relevant costs for this...
asked 16 minutes ago -
A car moving at 87 km/h has tires of 76 cm diameter. If the
vehicle comes...
asked 32 minutes ago -
Most of the galaxies in the universe are observed to be moving
away from Earth. Suppose...
asked 35 minutes ago -
Paired research designs, also sometimes referred to as repeated
measures designs, are associated with some common...
asked 34 minutes ago -
You working as a clinical engineer dealing with
autoclaves, xrays and life care machines, in what...
asked 36 minutes ago -
Explain in detail (not just enumerate) each of Koch’s
postulates to determine the etiology of a...
asked 48 minutes ago -
Assume ABC Company has asked you to not only prepare their 2017
year-end Balance Sheet but...
asked 46 minutes ago -
You have just had a new set of tires put on your car, and now
the...
asked 52 minutes ago -
Please answer ASAP 2) Choose a point at random from the unit
square [0, 1] ×...
asked 1 hour ago