Which of the following statements are equivalent? For all e > 0, there exists a ô > 0 such that |x – c| < 8 (and x E A) implies |f(x) – f(c)| < e V For all Ve f(c)), there exists a V;(c) such that x e V;(c) (and x E A) implies f(x) e Ve f(c)) V For all (xn) → c (with x, E A), it follows that f(xn) → f(c). limx»c f(x) = f(c)

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Q: Prove that Var(E(Y|X)) ≤ Var(Y)

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A: To verify that the given function is one -one onto from R to R (R= the set of real numbers)

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A: Our Aim is to tell the value of f(x+h) for the function f(x)=1x2+3-(i)

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A: To determine the value of the function f(7).

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A: Given  f(x) =x3+3x+17

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A: We will find the end behavior.

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.