4. The pdf of X is f(x) = 24 (27 - x³) for 0 < x < 3, and 0 otherwise. a) Find P(1 < X < 2). b) Find E(X). c) Find the third moment of X.

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A: We consider f(x)= x2

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A: The detailed solution is as follows below:

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A:

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A:

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A: We have given that the statement about to the probability density function (pdf) f(x).

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A: To find the f'(a) using definition of derivative

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Q: Name recognition A political candidate runs a weeklongseries of TV ads designed to attract public…

A: The hypotheses can be as follows: Null hypothesis: H0: Ads are not effective. Alternative…

Q: let f(x)= x2 . Find the value c in the interval (0,3) so that fave = f(c).

A:

Q: 3. Let f(x) = k/x 0<x<1 a) Find the value of k. b) Checking whether the given function is a pdf or…

A: For a function f(x) to be a valid pdf, following must be true. f(x)≥0   ∀ x ∫-∞∞f(x)dx=1 The…

Q: Let f(x) = cosx²) and g(x) = vx. The (natural) domain of (f • g)(x) is = Cos

A:

Q: If f is a positive function and f"(x) < 0 for a < xs b, show that T, < f(x) dx < M,

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Q: 5. Sketch the graph of one function f(x) that has all of the following properties: a.) f(-2) 0 b.)…

A: As per our guidelines we are supposed to answer  only one question. Here question 5) answer.

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A: Given :- To find all functions from X = a,b to Y= p,r,t.

Q: The function, f(x), in the graph below has f(1) = 1 and f'(1) = 2. Which of the following are the…

A: