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12. The Gumbel distribution is the distribution of log X with X Expo(1). Find the CDF...
explan the answer 10: A certain continuous distribution has cumulative distribution function (CDF) given by F(r)...
explan the answer
10: A certain continuous distribution has cumulative distribution function (CDF) given by F(r) 0, <0 where θ is an unknown parameter, θ > 0. (i) Find (a) the p.d.f., (b) the mean and (e) the variance of this distribution. (ii) Suppose that X (Xi, X2, Xn) is a random sample from this distribu- tion and let Y max(Xi, XXn). Find the CDF and p.d.f. of Y. Hence find the value of a for which EloY)
9. Let X have an exponential distribution with A 1 (see Question 5), and let Y...
9. Let X have an exponential distribution with A 1 (see Question 5), and let Y log(X). Find the probability density function of Y. Where is the density non-zero? Note that in this course, log refers to the log base e, or natural log, often symbolized In. The distribution of Y is called the (standard) Gumbel, or extreme value distribution.
2. Suppose that the CDF of X is given by Fur :53 e-3 for x <3 Fx)for 3 for r >3. 1 (a) Find the PDF of X and specify the support of X. (b) Given a standard uniform random variable U ~ unifo...
2. Suppose that the CDF of X is given by Fur :53 e-3 for x <3 Fx)for 3 for r >3. 1 (a) Find the PDF of X and specify the support of X. (b) Given a standard uniform random variable U ~ uniform(0, 1), find a transformation g) so that X g(U) has the above CDF. (Hint: This entails the quantile function F-().)
2. Suppose that the CDF of X is given by Fur :53 e-3 for x 3....
[25 points] Problem 4 - CDF Inversion Sampling ers coming from the U(0, 1) distribution into...
[25 points] Problem 4 - CDF Inversion Sampling ers coming from the U(0, 1) distribution into In notebook 12, we looked at one method many pieces of statistical software use to turn pseudorandom those with a normal distribution. In this problem we examine another such method. a) Simulating an Exponential i) The exponential distribution has pdf f(x) = le-ix for x > 0. Use the following markdown cell to compute by hand the cdf of the exponential. ii) The cdf...
For a random variable X with cumulative distribution function (cdf) Fx(x) = 1- (2/x)^2 ,x>2. (a).Find...
For a random variable X with cumulative distribution function (cdf) Fx(x) = 1- (2/x)^2 ,x>2. (a).Find the pdf fX(x). (b).Consider the random variable Y = X^2. Find the pdf of Y, fY (y).
3. Suppose that X has a Poisson distribution with mean μ=15. Use the 'cdf' command MTB...
3. Suppose that X has a Poisson distribution with mean μ=15. Use the 'cdf' command MTB > cdf; SUBC 〉 poisson 15. Find PX 〈 10)-[3] and P(15 X 20)= [3] 4. Suppose that Y has a hypergeometric distribution with parameters N = 20, M = 6, and n = 4, Use the command MTB > cdf 3; hypergeometric 20 6 4. a. [3] to find P(Y 53) = b. 3) Use the similar command to find P(Y > 2)...
The function below is a joint CDF of two continuous X, Y: iD else 1. Find the constant c and the ...
Please explain
The function below is a joint CDF of two continuous X, Y: iD else 1. Find the constant c and the marginal CDF Fx(u and Fy() 2. Are X, Y independent ? 3. Find the probabilities below: (a) p (X є (0.11, Ye (0,11 (b) p(X>0) (c) P(Y 1) (Hint: bound by a rectangle) (e) p(E), for the shaded area E in the figure.
The function below is a joint CDF of two continuous X, Y: iD else...
Consider the cumulative distribution function (cdf)F(y) =0, y≤0,y2,0< y≤1,11≤y. (a) Find E(Y) ifYhas this cdf. (b)...
Consider the cumulative distribution function (cdf)F(y) =0, y≤0,y2,0< y≤1,11≤y. (a) Find E(Y) ifYhas this cdf. (b) Find P(Y >1/3|Y≤2/3) ifYhas this cdf. (c) SupposeY1andY2are a random sample from this distribution. FindP(Y1≤1/2,Y2>1/2).
4. Let X be a Exponential random variable, X ~ Expo(2). Find the pdf of X3....
4. Let X be a Exponential random variable, X ~ Expo(2). Find the pdf of X3. [Hint: pdf of XP is not (pdf of X)3, find it by differentiating the cdf of X3, i.e., Px() = P(X® S2)]
Suppose that X has CDF Exercise 24.22. Suppose that X has CDF 0 If x <...
Suppose that X has CDF
Exercise 24.22. Suppose that X has CDF 0 If x < 0, İf 0 < x < 1, İf 1 < x < 7, a. Find the density fx(a) b. Find the median of X
explan the answer
10: A certain continuous distribution has cumulative distribution function (CDF) given by F(r) 0, <0 where θ is an unknown parameter, θ > 0. (i) Find (a) the p.d.f., (b) the mean and (e) the variance of this distribution. (ii) Suppose that X (Xi, X2, Xn) is a random sample from this distribu- tion and let Y max(Xi, XXn). Find the CDF and p.d.f. of Y. Hence find the value of a for which EloY)
9. Let X have an exponential distribution with A 1 (see Question 5), and let Y log(X). Find the probability density function of Y. Where is the density non-zero? Note that in this course, log refers to the log base e, or natural log, often symbolized In. The distribution of Y is called the (standard) Gumbel, or extreme value distribution.
2. Suppose that the CDF of X is given by Fur :53 e-3 for x <3 Fx)for 3 for r >3. 1 (a) Find the PDF of X and specify the support of X. (b) Given a standard uniform random variable U ~ uniform(0, 1), find a transformation g) so that X g(U) has the above CDF. (Hint: This entails the quantile function F-().)
2. Suppose that the CDF of X is given by Fur :53 e-3 for x 3....
[25 points] Problem 4 - CDF Inversion Sampling ers coming from the U(0, 1) distribution into In notebook 12, we looked at one method many pieces of statistical software use to turn pseudorandom those with a normal distribution. In this problem we examine another such method. a) Simulating an Exponential i) The exponential distribution has pdf f(x) = le-ix for x > 0. Use the following markdown cell to compute by hand the cdf of the exponential. ii) The cdf...
3. Suppose that X has a Poisson distribution with mean μ=15. Use the 'cdf' command MTB > cdf; SUBC 〉 poisson 15. Find PX 〈 10)-[3] and P(15 X 20)= [3] 4. Suppose that Y has a hypergeometric distribution with parameters N = 20, M = 6, and n = 4, Use the command MTB > cdf 3; hypergeometric 20 6 4. a. [3] to find P(Y 53) = b. 3) Use the similar command to find P(Y > 2)...
Please explain
The function below is a joint CDF of two continuous X, Y: iD else 1. Find the constant c and the marginal CDF Fx(u and Fy() 2. Are X, Y independent ? 3. Find the probabilities below: (a) p (X є (0.11, Ye (0,11 (b) p(X>0) (c) P(Y 1) (Hint: bound by a rectangle) (e) p(E), for the shaded area E in the figure.
The function below is a joint CDF of two continuous X, Y: iD else...
4. Let X be a Exponential random variable, X ~ Expo(2). Find the pdf of X3. [Hint: pdf of XP is not (pdf of X)3, find it by differentiating the cdf of X3, i.e., Px() = P(X® S2)]
Suppose that X has CDF
Exercise 24.22. Suppose that X has CDF 0 If x < 0, İf 0 < x < 1, İf 1 < x < 7, a. Find the density fx(a) b. Find the median of X
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