3.4 Solve the below problem:Let Y, and Y, have a bivariate normal distribution:f(V1. Y2)exp+2(1-p2)01-00 < y1 < 00,-00 < y2 < 00,Show that the marginal distribution of Y, is normal with mean µz and variance o is givenby:1f(y2) =203,-00 < y2 < o0V2no2

3.4 Solve the below problem: Let Y, and Y, have a bivariate normal distribution: expl- ) - 20 (*)() + ()| 1 Y2-H2 2-42 f(V1. Y2) = -2p 2no,021-p -00 < yı < o, -00 < y2 < o, Show that the marginal distribution of Y2 is normal with mean µ2 and variance o is given by: 1 203 ,-00 < y2 < ∞ V2no2

3.4 Solve the below problem: Let Y, and Y, have a bivariate normal distribution: expl- ) - 20 (*)() + ()| 1 Y2-H2 2-42 f(V1. Y2) = -2p 2no,021-p -00 < yı < o, -00 < y2 < o, Show that the marginal distribution of Y2 is normal with mean µ2 and variance o is given by: 1 203 ,-00 < y2 < ∞ V2no2

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

See similar textbooks

Related questions

Q: (d) Suppose it had previously been believed that when air void increased by 1 percent, the…

Q: 4. Suppose the variance of X is 2.0091. Which of the following is(are) TRUE? L In the long run, the…

Q: Suppose that x has a beta distribution with parameters a = 2.5 and B = 1. Determine to 4 decimal…

A: Given X has a beta distribution having parameters α =2.5 and β=1 So, the distribution of X can be…

Q: Suppose you have a sample of size n for variables X and Y. The sample covariance of X and Y is…

Q: Example 9-32. Show that the mean value of positive square root of a y (u) variate is T(u +;)/T(u).…

Q: 8. Show that the m.g.f. about the mean for a Poisson variate is exp {m (e-t-1). Obtain from this the…

Q: 3.139 In the daily production of a certain kind of rope, the number of defects per foot Y is assumed…

A: Here are some properties of expectation of a random variable. We will make use of these properties…

Q: Suppose that x has a beta distribution with parameters a = 2.2 and B = 1. Determine to 4 decimal…

A: Given that, X has a beta distribution with parameters α = 2.2, β= 1.

Q: Suppose Y₁, Y2,, Yn is an iid sample from a gamma population distribution with shape parameter a = 2…

Q: 10. Suppose that X . . , X, form a random sample from the normal distribution with mean 0 and…

Q: Suppose the proportion X of surface area in a randomly selected quadrat that is covered by a certain…

A: Given:X follows beta distribution with parameter α=4 and β=2. X~Beta(α,β) X~Beta(4,2)

Q: Suppose that x has a beta distribution with parameters a = 2.4 and ß = 1. Determine to 4 decimal…

A: Solution

Q: Suppose that x has a beta distribution with parameters a = 2.7 and ß = 1. Determine to 4 decimal…

Q: 3. Given û=E(Y₁-B₁-B₂X)² derive the normal equations and eventually the estimation equations for B₁…

A: Differentiate the given quantity with respet to both coefficient respectively and equates to zero…

Q: 7.9 Let X1,...,Xn be iid with pdf f(x|e) : * 0 0. Estimate 0 using both the method of moments and…

Q: Suppose X has a gamma distribution with the following parameters: mean u- 41.5692 ms B = o /u =…

Q: A random sample of n1 = 14 winter days in Denver gave a sample mean pollution index x1 = 43.…

Q: 2. Calculate the mean and the variance of the normal distribution N(u,02) from its moment generating…

A: We need to calculate the mean and variance of the normal distribution N( μ,σ2) from its moment…

Q: Suppose we want to test the hypothesis of Ho : u 2 1 versus H. : u < 1, and a random sample of n =…

A: Given data : sample size, n = 49 sample mean, x̄ = -1.0 sample standard…

Q: 4. Suppose the variance of X is 2.0091. Which of the following is(are) TRUE? I. In the long run, the…

Q: Let X~N(0, 0?). Find the CRLB for variances of the unbiased estimator of T(0)= 0²

A: Given N~(0,θ2), t(θ)=θ2

Q: 2.) Find the Equation Of the normal line to the wrue y= 3x-2x +1 at P( 1,2)

A: Topic = Derivative

Q: 5.7.2 Let Y1, Y2,..., Yn be a random sample of size n from a normal pdf having µ = 0. Show that S…

Q: 4. Let X~N(0, e?). Find the CRLB for variances of the unbiased estimator of T(0)= 0. 5. Let X-f(x;…

A: Given that We have to find the MLE of theta :

Q: 4.5.11. Let Y₁ 1 is accepted if the observed Y₁ 2 A (a) Find the constant c so that the…

Q: If X, and X2 are the means of independent random sample of sizes n and n2 from a normal population…

A: Minimum varience of the estimator w*x1bar+(1-w)*x2bar is sigma^2/(n-1+n2) And value of w at which…

Q: 5. Suppose that X1, X2, .. ,X, are an iid sample from the distribution given below, f(X)e = (1/2)(1+…

Q: 0 p.m.with a standard deviation of Rs. 60, and a random sample of 1,000 rom another State gives the…

A: We have given that Sample sizes n1=1200 , n2=1000 Sample means X̄1=400 , X̄2=500…

Q: 8. Let x be a random variable that represents the hemoglobin count (HC) in human blood (measured in…

A: mu = 14.2 xbar =15.1 s=2.5 n =10

Q: Given the following time series Y: Y; = 1.5 + Y,-1 + E; (a) Examine the stationarity of Y. (b) Apply…

A: According to the given problem; Yt=1.5+Yt-1+εt =1.5+EYt-1+Eεt Eεt =0Yt=1.5+EYt-1 which is…

Q: If X follows a gamma distribution with a mean of 12 and a standard deviation of 6 then the parameter…

A: gamma distribution : mean= αβ standard deviation=β√α

Q: 11. Find out the likely production corresponding to a rainfall of 40 cms. from the following däta :…

A: Regression: By regression we mean estimation or prediction of the average value of one variable for…

Q: A snack food manufacturer estmates that the variance of the number of grams of carbohydrates in…

A: Given, Random sample is 22. Sample variance is 1.08 Population variance is 1.22. a) Hypotheses:…

Q: Suppose that x has a beta distribution with parameters a = 2.8 and B = 1. Determine to 4 decimal…

Q: i.i.d. 8. Consider a normal random variable X N(H,o2) and a corresponding random sample {x1, ..,…

Q: s 19·13. The average number of articles produced by two machines per day are 200 and 250 with…

Q: Suppose that x has a beta distribution with parameters a = 2.9 and B = 1. Determine to 4 decimal…

A: Given : α = 2.9β = 1

Q: Consider a random sample of size n drawn from a population with mean Hx and variance o. Show that:…

Q: A sample of 50 student ages is taken from a bell-shaped population with a mean age (µ) of 21.2 years…

A: We have given that Sample size=n=50 Mean=mu=21.2 Standard deviation=sigma=2.8…

Q: D.1.2 Test the hypothesis that the average content of containers of a particular lubricant is 10…

A: Given n=10 X-bar=10.04

Q: In the daily production of a certain kind of rope, the number of defects per foot given by Y is…

Q: 17. A 20,000-piece manufacturing run of 2200 resistors has a mean value of 2200 (naturally!) and a…

A: Given information: μ=220 Ωσ=2.5 ΩTolerance level=2%N=20,000 Note: Ω symbol is shown as 0 in the…

Q: A random sample of n1 = 11 winter days in Denver gave a sample mean pollution index x1 = 43.…

A: a) The level of significance is 0.01.

Q: Suppose X1, ..., Xn have been randomly sampled from a normal distribution with mean 0 and unknown…

Q: 2- The test score is now normalised to have a mean of 0 and a standard deviation of 1. Using the…

Q: 4.54 Figure 4.16 shows a randomization distribution for testing Ho =2 versus H u1 # H2. The…

A: When the critical area of distribution is two-sided, a two-tailed test method is used. Given: The…

Q: Suppose that x has a beta distribution with parameters a = 2.1 and B = 1. Determine to 4 decimal…

Q: 3.4 Solve the below problem: Let Y, and Y, have a bivariate normal distribution: -20 ()() + ()) 1…

A: Joint Probability Distribution: Let X and Y be two continuous random variables defined over the…

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

3.4 Solve the below problem:
Let Y, and Y, have a bivariate normal distribution:
f(V1. Y2)
exp
+
2(1-p2)
01
-00 < y1 < 00,
-00 < y2 < 00,
Show that the marginal distribution of Y, is normal with mean µz and variance o is given
by:
1
f(y2) =
203
,-00 < y2 < o0
V2no2

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 7 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

If X1 and X2 constitute a random sample of size n = 2from an exponential population, find the efficiency of 2Y1relative to X, where Y1 is the first order statistic and 2Y1and X are both unbiased estimators of the parameter
A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.33. A dietician is asked to test this claim and finds that a random sample of 24 servings has a variance of 1.37. At α=0.01, is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed. Complete parts (a) through (e) below. (a) Write the claim mathematically and identify H0 and Ha. A. H0: σ2≤1.33 (Claim) Ha: σ2>1.33 B. H0: σ2≠1.33 Ha: σ2=1.33 (Claim) C. H0: σ2≥1.33 Ha: σ2<1.33 (Claim) D. H0: σ2=1.33 (Claim) Ha: σ2≠1.33 (b) Find the critical value(s) and identify the rejection region(s). The critical value(s) is(are) enter your response here. (Round to two decimal places as needed. Use a comma to separate answers as needed.) Choose the correct statement below and fill in the corresponding answer boxes. A. The…
If the PDF of X is f(x)=2x/k2 for 0<x<k, for what value of k is the variance of X equal to 2?
Suppose X1, ..., Xn have been randomly sampled from a normal distribution with mean 0 and unknown variance sigma^2, and let U = c * i=1 -> n summation (X_ i)^2 , where c is a constant. Find the value of c that minimises the Mean Squared Error (MSE)
Suppose X, Y, Z are i.i.d. from a Normal distribution with mean μ and variance 4. You have to compare between three estimators for μ, which are T1:= (2X + Y)/3 , T2:= (X + Y − Z)/2 , T3:= (Y + 2Z)/2 . (a) Which among the above are unbiased estimators for μ? (b) Which among these have the smallest variance? (c) Can you propose an estimator for μ which is better than the 3 above? You have to show that your estimator is indeed better.
D.1.2 Test the hypothesis that the average content of containers of a particular lubricant is 10 liters if the contents of a random sample of 10 containers are 10.2, 9.7, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.13, and 9.8 liters. Use α 0.01 level of significance and assume that the distribution of contents is normal.
The desired percentage of SiO2 in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO2 in a sample is normally distributed with ? = 0.32 and that x = 5.21. (Use ? = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5?State the appropriate null and alternative hypotheses. H0: ? = 5.5Ha: ? ≠ 5.5H0: ? = 5.5Ha: ? ≥ 5.5 H0: ? = 5.5Ha: ? < 5.5H0: ? = 5.5Ha: ? > 5.5 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage.Reject the null hypothesis. There is sufficient evidence…
Suppose you have a sample of size n for variables X and Y. The sample covariance of X and Y is Cov(X,Y) = 1,000, the sample standard deviation for X is Sx=20 and the sample standard deviation for Y is SY=75. What is the sample correlation coefficient, r?
Assume X_1, X_2, .....X_n are random samples from X~Exponential(θ).1) Find the MLE estimator of θ .
Are the following results significant at α=.01? F(2,27) =10.56, p=.02 Yes No 2. A large F-ratio (or a significant result) is the result of: a small amount variability within the groups and a large amount of variability between the groups a large amount variability within the groups and a small amount of variability between the groups a large amount variability within the groups and a large amount of variability between the groups a small amount variability within the groups and a small amount of variability between the groups
Consider the following two formulations of the bivariate PRF, where ui and εi are both mean-0 stochastic disturbances (i.e random errors): yi = β0 + β1xi + u yi = α0 + α1(xi − x¯) + ϵ a) Write the OLS estimators of β1 and α1. Are the two estimators the same? b) What is the advantage, if any, of the second model over the first?