For each n ∈ N, let f_n(x) = a_nx + b_n where a_n,b_n are sequences of...

For each n ∈ N, let f_n(x) = a_nx + b_n where a_n,b_n are sequences of real numbers. Prove that if f_n → f on [0,1] where f is a function on [0,1], then the convergence is necessarily uniform.

Expert Solution

First we find the function f by using the pointwise convergence .then we proceed for uniform convergence of sequence fn.

Colby Messinger answered 1 year ago

Let f(x) = {(C/x^n if 1≤ x <∞; 0 elsewhere)} where n is an integer >1....

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The question is correct. Let X be an n-element set of positive integers each of whose...

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Let X have a binomial distribution with parameters n = 25 and p. Calculate each of...

Let X have a binomial distribution with parameters n = 25 and p. Calculate each of the following probabilities using the normal approximation (with the continuity correction) for the cases p = 0.5, 0.6, and 0.8 and compare to the exact binomial probabilities calculated directly from the formula for b(x; n, p). (Round your answers to four decimal places.) (a) P(15 ≤ X ≤ 20) p P(15 ≤ X ≤ 20) P(14.5 ≤ Normal ≤ 20.5) 0.5 1 2 0.6...

Let X have a binomial distribution with parameters n = 25 and p. Calculate each of...

Let X have a binomial distribution with parameters n = 25 and p. Calculate each of the following probabilities using the normal approximation (with the continuity correction) for the cases p = 0.5, 0.6, and 0.8 and compare to the exact binomial probabilities calculated directly from the formula for b(x; n, p). (Round your answers to four decimal places.) P(20 ≤ X) p P(20 ≤ X) P(19.5 ≤ Normal) 0.5 0.6 0.8

Let X have a binomial distribution with parameters n = 25 and p. Calculate each of...

Let X have a binomial distribution with parameters n = 25 and p. Calculate each of the following probabilities using the normal approximation (with the continuity correction) for the cases p = 0.5, 0.6, and 0.8 and compare to the exact binomial probabilities calculated directly from the formula for b(x; n, p). (Round your answers to four decimal places.) (a) P(15 ≤ X ≤ 20) p P(15 ≤ X ≤ 20) P(14.5 ≤ Normal ≤ 20.5) 0.5 0.6 0.8 (B)P(X...

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Question

For each n ∈ N, let f_n(x) = a_nx + b_n where a_n,b_n are sequences of...

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Expert Solution

Related Solutions

Let f(x) = {(C/x^n if 1≤ x <∞; 0 elsewhere)} where n is an integer >1....

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