Let X(1) 0. a) Show that X4) and X(6) – X() are independent for any s>r. b) Find the distribution of Xr+1) – X(r)-

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A: Let , where and

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A:

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A: f(x)=2x ; 0&lt; x&lt; 1 n be the sample size

Q: Let X ∼ N(2, 4). (a) What is the distribution of (X−2) /2 ?

A:

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A: From the given information we want to graph graph of cumulative distribution function.

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A:

Q: Let X~ N(0, 1) and let Y = -X. (a) Show that Y~ N(0, 1) (by showing that Y has cdf Þ). (b) What is…

A: X follows a standard normal distribution.

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A: Let X1, X2,.......Xn be the random sample having Uniform distribution (0,1)Y1=min{X1,…

Q: None

A: Step 1: Step 2: Step 3: Step 4:

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A: Solution

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A: Range(x) = Max(x) - Min(x) First we need to find the PDFs of max(X) and min(X).

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Q: In statistics, the range is computed as the difference between the minimum and maximum values…

A: Range is equal to maximum value minus minimum value

Q: Let x1 ~ N(0,1), X2 ~N(-1,4) and X3~N(1,9) be independent.  Derive the distribution of Y=x1-x2-2x3…

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A: