- Fill In The Missing Pieces 1 (60.07 KiB) Viewed 21 times
Fill in the missing pieces:
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answerhappygod
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Fill in the missing pieces:
Fill in the missing pieces:
Let X be a random variable with Var(x)=0?. Then my possible sample of n independent values is represented as X1, X2, X3, , Xn each with Var(Xi) = o. Part 1: the constant denominator Consider the sample average X X1 + X2 + ... + X. Rewrite slightly as (X1 + X2 + ... + Xn) n 1 is like the constant a b from useful property #2. n This means that I can rewrite Var - ((x2 + x2 + ... + x) ) as n Var(X1 + X2 + ... + Xn) + 1 Here the first blank 1 n2 10 Var Var(X) n2 12 --() -(1) 1 1 And the second blank 10 Var - Var(X) n n Part 2: Let's focus on the Variance of the sum of samples. To compute Var(X1 + X2 + ... + Xn) we can apply property #1, since X1, X2, ..., X, are identical independent constants variables disjoint Property #1 indicates that Var(X1 + X2 + ... + Xn) CO2 Var(xi) Var(X1) + Var(X2) + ... + Var(X) Then, since Var(X;) op for each of the n independent samples, we can simplify to find that Var(X1 + X2 + ... + Xn) Geung nở Putting Part 1 and Part 2 together and simplifying, it follows that Var(X) = o + 1 n? n o 90 n + = | ۹۵ | ۹۰ / n2 no
Let X be a random variable with Var(x)=0?. Then my possible sample of n independent values is represented as X1, X2, X3, , Xn each with Var(Xi) = o. Part 1: the constant denominator Consider the sample average X X1 + X2 + ... + X. Rewrite slightly as (X1 + X2 + ... + Xn) n 1 is like the constant a b from useful property #2. n This means that I can rewrite Var - ((x2 + x2 + ... + x) ) as n Var(X1 + X2 + ... + Xn) + 1 Here the first blank 1 n2 10 Var Var(X) n2 12 --() -(1) 1 1 And the second blank 10 Var - Var(X) n n Part 2: Let's focus on the Variance of the sum of samples. To compute Var(X1 + X2 + ... + Xn) we can apply property #1, since X1, X2, ..., X, are identical independent constants variables disjoint Property #1 indicates that Var(X1 + X2 + ... + Xn) CO2 Var(xi) Var(X1) + Var(X2) + ... + Var(X) Then, since Var(X;) op for each of the n independent samples, we can simplify to find that Var(X1 + X2 + ... + Xn) Geung nở Putting Part 1 and Part 2 together and simplifying, it follows that Var(X) = o + 1 n? n o 90 n + = | ۹۵ | ۹۰ / n2 no
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