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help with part b. please!!
4) Suppose X and si are the mean and variance of...
Hello can someone help me answer this please Suppose that X (X1,X2, . . . ,...
Hello can someone help me answer this please
Suppose that X (X1,X2, . . . , X.) ald Y-(Yİ,%, , Y,n) are random samples from continuous distributions F and G, respectively. Wilcoxon's two-sample test statistioc W- W(X,Y) is defined to be X/Ri where Ri is the rank of Y in the combined sample. 1. Let T Z, where Z, Z2,, Zm are numbers sampled at random without replacement from the set {1,2,...,N) Show that E(Z) = (N + 1)/2 and...
Suppose that Xi are IID normal random variables with mean 2 and variance 1, for i...
Suppose that Xi are IID normal random variables with mean 2 and variance 1, for i = 1, 2, ..., n. (a) Calculate P(X1 < 2.6), i.e., the probability that the first value collected is less than 2.6. (b) Suppose we collect a sample of size 2, X1 and X2. What is the probability that their sample mean is greater than 3? (c) Again, suppose we collect two samples (n=2), X1 and X2. What is the probability that their sum...
x, and S1 are the sample mean and sample variance from a population with mean μ|...
x, and S1 are the sample mean and sample variance from a population with mean μ| and variance ơf. Similarly, X2 and S1 are the sample mean and sample variance from a second population with mean μ and variance σ2. Assume that these two populations are independent, and the sample sizes from each population are n,and n2, respectively. (a) Show that X1-X2 is an unbiased estimator of μ1-μ2. (b) Find the standard error of X, -X. How could you estimate...
Suppose X, and X, are ramdom samples drawn from a population with mean ji and variance...
Suppose X, and X, are ramdom samples drawn from a population with mean ji and variance o?. Denote X = (1 - a)X1 +aX2. Find the value of a which minimize the variance of X. O1 O o 2 OO QUESTION 7 Let (X1, X2, ..., X16} be a random sample of size 16 from a normal pop- ulation having a mean of . The sample variance equals to 4. You want to test: HNS 4 versus H : >...
3. You have two independent random samples: XiXX from a population with mean In and variance σ2 a...
3. You have two independent random samples: XiXX from a population with mean In and variance σ2 and Y, Y2, , , , , Y,n from a population with mean μ2 and variance σ2. Note that the two populations share a common variance. The two sample variances are Si for the first sample and Si for the second. We know that each of these is an unbiased estimator of the common population variance σ2, we also know that both of...
Please ignore part abc 4. Suppose that (X1, Yİ), , (XN,Yv) denotes a random sample. Let Si = a + bX, T, e+ dy, where a, b, c and d are constants. Let X ΣΧ, and σ2-NL Σ(x,-x)2, with the analogous expr...
Please ignore part abc
4. Suppose that (X1, Yİ), , (XN,Yv) denotes a random sample. Let Si = a + bX, T, e+ dy, where a, b, c and d are constants. Let X ΣΧ, and σ2-NL Σ(x,-x)2, with the analogous expressions for y S, T. Let σΧΥ-ΝΤΣ (Xi-X)(X-Y), and let P:XY ƠXY/(ƠXƠY), with the analogous expressions for S, T. (a) Show that σ bbe (b) Show that ớsı, d ớx (c) Show that psT ST (d) How do the...
I need help on this, please help me Suppose that X = (Xi, X2, , Xn)...
I need help on this, please help me
Suppose that X = (Xi, X2, , Xn) and Y = (Yİ, ½, . . . ,Yn) are randon samples from continuous distributions F and G, respectively. Wilcoxon's two-sample test statistic W W(X,Y) is defined to be Σǐ1+nn 1 R d n+m where Ri is the rank of Yn the combine sample. 2. Show that W can be written as where U is the number of pairs (X,, Y) with X, <...
I. Suppose population 1 has mean μί with variance σ2 and population 2 has mean μ2...
I. Suppose population 1 has mean μί with variance σ2 and population 2 has mean μ2 with the same variance σ2. Let s and s denote the sample variances from two samples with size ni and n2 from the corresponding populations, respectively. Show that the pooled estimator 1i+(2-1)si pooled ni + n2 -2 is an unbiased estimator of σ2.
4 and 5 samples, the other in small samples. Which is which? Explain. (d) Suppose we...
4
and 5
samples, the other in small samples. Which is which? Explain. (d) Suppose we know that the 5 values are from a symmetric distribution. Then the sample median is also unbiased and consistent for the population mean. The sample mean has lower variance. Would you prefer to use the sample 4. Suppose Yi, Y, are iid r ables with E(n)-μ, Var(K)-σ2 < oo. For large n, find the approximate 5. Suppose we observe Yi...Yn from a normal distribution...
Suppose population l has mean ,11 with variance σ2 and population 2 has mean Ha with...
Suppose population l has mean ,11 with variance σ2 and population 2 has mean Ha with the same variance σ2. Let s' and s denote the sample variances from two samples with size n and n2 from the corresponding populations, respectively. Show that the pooled estimator (m-1)sit (n2-1)d ni t n22 pooled is an unbiased estimator of σ2
Hello can someone help me answer this please
Suppose that X (X1,X2, . . . , X.) ald Y-(Yİ,%, , Y,n) are random samples from continuous distributions F and G, respectively. Wilcoxon's two-sample test statistioc W- W(X,Y) is defined to be X/Ri where Ri is the rank of Y in the combined sample. 1. Let T Z, where Z, Z2,, Zm are numbers sampled at random without replacement from the set {1,2,...,N) Show that E(Z) = (N + 1)/2 and...
Suppose that Xi are IID normal random variables with mean 2 and variance 1, for i = 1, 2, ..., n. (a) Calculate P(X1 < 2.6), i.e., the probability that the first value collected is less than 2.6. (b) Suppose we collect a sample of size 2, X1 and X2. What is the probability that their sample mean is greater than 3? (c) Again, suppose we collect two samples (n=2), X1 and X2. What is the probability that their sum...
x, and S1 are the sample mean and sample variance from a population with mean μ| and variance ơf. Similarly, X2 and S1 are the sample mean and sample variance from a second population with mean μ and variance σ2. Assume that these two populations are independent, and the sample sizes from each population are n,and n2, respectively. (a) Show that X1-X2 is an unbiased estimator of μ1-μ2. (b) Find the standard error of X, -X. How could you estimate...
Suppose X, and X, are ramdom samples drawn from a population with mean ji and variance o?. Denote X = (1 - a)X1 +aX2. Find the value of a which minimize the variance of X. O1 O o 2 OO QUESTION 7 Let (X1, X2, ..., X16} be a random sample of size 16 from a normal pop- ulation having a mean of . The sample variance equals to 4. You want to test: HNS 4 versus H : >...
3. You have two independent random samples: XiXX from a population with mean In and variance σ2 and Y, Y2, , , , , Y,n from a population with mean μ2 and variance σ2. Note that the two populations share a common variance. The two sample variances are Si for the first sample and Si for the second. We know that each of these is an unbiased estimator of the common population variance σ2, we also know that both of...
Please ignore part abc
4. Suppose that (X1, Yİ), , (XN,Yv) denotes a random sample. Let Si = a + bX, T, e+ dy, where a, b, c and d are constants. Let X ΣΧ, and σ2-NL Σ(x,-x)2, with the analogous expressions for y S, T. Let σΧΥ-ΝΤΣ (Xi-X)(X-Y), and let P:XY ƠXY/(ƠXƠY), with the analogous expressions for S, T. (a) Show that σ bbe (b) Show that ớsı, d ớx (c) Show that psT ST (d) How do the...
I need help on this, please help me
Suppose that X = (Xi, X2, , Xn) and Y = (Yİ, ½, . . . ,Yn) are randon samples from continuous distributions F and G, respectively. Wilcoxon's two-sample test statistic W W(X,Y) is defined to be Σǐ1+nn 1 R d n+m where Ri is the rank of Yn the combine sample. 2. Show that W can be written as where U is the number of pairs (X,, Y) with X, <...
I. Suppose population 1 has mean μί with variance σ2 and population 2 has mean μ2 with the same variance σ2. Let s and s denote the sample variances from two samples with size ni and n2 from the corresponding populations, respectively. Show that the pooled estimator 1i+(2-1)si pooled ni + n2 -2 is an unbiased estimator of σ2.
4
and 5
samples, the other in small samples. Which is which? Explain. (d) Suppose we know that the 5 values are from a symmetric distribution. Then the sample median is also unbiased and consistent for the population mean. The sample mean has lower variance. Would you prefer to use the sample 4. Suppose Yi, Y, are iid r ables with E(n)-μ, Var(K)-σ2 < oo. For large n, find the approximate 5. Suppose we observe Yi...Yn from a normal distribution...
Suppose population l has mean ,11 with variance σ2 and population 2 has mean Ha with the same variance σ2. Let s' and s denote the sample variances from two samples with size n and n2 from the corresponding populations, respectively. Show that the pooled estimator (m-1)sit (n2-1)d ni t n22 pooled is an unbiased estimator of σ2
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