Considering two Gaussian distributions N1~(μ1,σ1^2) and N2~(μ2,σ2^2), we pick two random variables x1 and x2 in...
Considering two Gaussian distributions N1~(μ1,σ1^2) and N2~(μ2,σ2^2), we pick two random variables x1 and x2 in order to compute the sum x3=x1+x2. We want to prove that:
a) x3 follows a gaussian distribution
b) estimate mean value μ3 and variance σ3^2
c) repeat the above steps for multivariate Gaussian distributions N1~(μ1,Σ1) and N2~(μ2,Σ2)
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Considering two Gaussian distributions N1~(μ1,σ1^2) and
N2~(μ2,σ2^2), we pick two random variables x1 and x2 in...
Find the standardized test statistic to test the claim that μ1 ≠ μ2. Assume the two...
Find the standardized test statistic to test the claim that μ1 ≠ μ2. Assume the two samples are random and independent. Population statistics: σ1 = 0.76 and σ2 = 0.51 Sample statistics: x1 = 3.6, n1 = 51 and x2 = 4, n2 = 38
Consider the following hypothesis test. H0: μ1 − μ2 = 0 Ha: μ1 − μ2 ≠...
Consider the following hypothesis test. H0: μ1 − μ2 = 0 Ha: μ1 − μ2 ≠ 0 The following results are for two independent samples taken from the two populations. Sample 1 Sample 2 n1 = 80 n2 = 70 x1 = 104 x2 = 106 σ1 = 8.4 σ2 = 7.2 (a) What is the value of the test statistic? (Round your answer to two decimal places.) (b) What is the p-value? (Round your answer to four decimal places.)...
Find the critical value to test the claim that μ1 < μ2. Two samples are random,...
Find the critical value to test the claim that μ1 < μ2. Two samples are random, independent, and come from populations that are normal. The sample statistics are given below. Assume that σ 2/1= σ2/2. Use α = 0.05. n1 = 15 n2 = 15 x1 = 25.74 x2 = 28.29 s1 = 2.9 s2 = 2.8
Give a 95% confidence interval, for μ1−μ2μ1-μ2 given the following information. n1=45n1=45, ¯x1=2.67x¯1=2.67, s1=0.69s1=0.69 n2=20n2=20, ¯x2=2.8x¯2=2.8,...
Give a 95% confidence interval, for μ1−μ2μ1-μ2 given the following information. n1=45n1=45, ¯x1=2.67x¯1=2.67, s1=0.69s1=0.69 n2=20n2=20, ¯x2=2.8x¯2=2.8, s2=0.61s2=0.61 <μ1−μ2
I. Suppose population 1 has mean μ1 with variance σ2 and population 2 has mean μ2...
I. Suppose population 1 has mean μ1 with variance σ2 and population 2 has mean μ2 denote the sample variances from two samples with the same variance σ2 Let s and s with size n and n2 from the corresponding populations, respectively. Show that the pooled estimator pooled n1 2 - 2 is an unbiased estimator of σ2
Give a 99.8% confidence interval, for μ1−μ2μ1-μ2 given the following information. n1=60n1=60, ¯x1=2.05x¯1=2.05, s1=0.61s1=0.61 n2=20n2=20, ¯x2=2.44x¯2=2.44,...
Give a 99.8% confidence interval, for μ1−μ2μ1-μ2 given the following information. n1=60n1=60, ¯x1=2.05x¯1=2.05, s1=0.61s1=0.61 n2=20n2=20, ¯x2=2.44x¯2=2.44, s2=0.48s2=0.48 ±± Rounded to 2 decimal places.
Suppose we have taken independent, random samples of sizes n1 = 7 and n2 = 7...
Suppose we have taken independent, random samples of sizes n1 = 7 and n2 = 7 from two normally distributed populations having means μ1 and μ2, and suppose we obtain x1=240, x2=210, s1=5, and s2 = 6 Use critical values and p-values to test the null hypothesis H0: μ1 − μ2 ≤ 20 versus the alternative hypothesis Ha: μ1 − μ2 > 20 by setting α equal to .10. How much evidence is there that the difference between μ1 and...
. If X1, X2,..., Xn are independent random variables with common mean μ and variances σ1,...
. If X1, X2,..., Xn are independent random variables with common mean μ and variances σ1, σ2, . . ., σα , prove that Σί (Xi-T)2/[n(n-1)] is an ว. 102n unbiased estimate of var[X] 3. Suppose that in Exercise 2 the variances are known. LeTw Σί uiXi
Consider the hypothesis test H0:μ1=μ2 against H1:μ1<μ2 with known variances σ1=10 and σ2=5. Suppose that sample...
Consider the hypothesis test H0:μ1=μ2 against H1:μ1<μ2 with
known variances σ1=10 and σ2=5. Suppose that sample sizes n1=10 and
n2=15 and that x¯1=14.2 and x¯2=19.7. Use α=0.05.
Font Paragraph Styles Chapter 10 Section 1 Additional Problem 1 Consider the hypothesis test Ho : = 12 against HI : <H2 with known variances = 10 and 2 = 5. Suppose that sample sizes nj = 10 and 12 = 15 and that I = 14.2 and 72 = 19.7. Use a...
Let X1 and X2 be independent random variables with mean μ and variance σ2. Suppose we...
Let X1 and X2 be independent random variables with mean μ and variance σ2. Suppose we have two estimators 1 (1) Are both estimators unbiased estimatros for θ? (2) Which is a better estimator?
I. Suppose population 1 has mean μ1 with variance σ2 and population 2 has mean μ2 denote the sample variances from two samples with the same variance σ2 Let s and s with size n and n2 from the corresponding populations, respectively. Show that the pooled estimator pooled n1 2 - 2 is an unbiased estimator of σ2
. If X1, X2,..., Xn are independent random variables with common mean μ and variances σ1, σ2, . . ., σα , prove that Σί (Xi-T)2/[n(n-1)] is an ว. 102n unbiased estimate of var[X] 3. Suppose that in Exercise 2 the variances are known. LeTw Σί uiXi
Consider the hypothesis test H0:μ1=μ2 against H1:μ1<μ2 with
known variances σ1=10 and σ2=5. Suppose that sample sizes n1=10 and
n2=15 and that x¯1=14.2 and x¯2=19.7. Use α=0.05.
Font Paragraph Styles Chapter 10 Section 1 Additional Problem 1 Consider the hypothesis test Ho : = 12 against HI : <H2 with known variances = 10 and 2 = 5. Suppose that sample sizes nj = 10 and 12 = 15 and that I = 14.2 and 72 = 19.7. Use a...
Let X1 and X2 be independent random variables with mean μ and variance σ2. Suppose we have two estimators 1 (1) Are both estimators unbiased estimatros for θ? (2) Which is a better estimator?
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