A continuous random variable X has the probability density function0,hx - h,3h-hx,0,which can be graphed asf(x)hf(x) =x < 11≤x≤22≤ x ≤ 3x > 32 3X(a) Find h which makes f(x) a valid probability density function.(b) Find the cumulative distribution function F(x).

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Answered: A continuous random variable X has the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose that the continuous random variable X has cumulative distribution function given by F(x)= 0, if x < sqrt(2); x2-2, if sqrt(2) <= x <= sqrt(3); 1, if sqrt(3) <= x Find the probability density function of X.
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Define the quartiles of a probability function to be those values a₁, a₂ and a 3 1 4 P(-∞⁰ < x≤ a₁) = P(a₁ ≤ x ≤ a₂) = P(a₂ ≤ x ≤ a3) = P(a3 ≤ x < ∞) < 1 function p(x) π(1 + x²) a₁ = a2 a3 = = = such that Find the quartile values for the probability
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A random variable has probability density function f(x) = 30x (1 - x) <(0 < xs 1). Compute its cumulative distribution F(x). O 10x3- 15x4 + 6x5 + 1 O 30x(1 - x) O 30x2 - 60x3 + 30x4 O 10x3 - 15x4 + 6x5 O none of these A Moving to the next question prevents changes to this answer. to search 63°F S End F10 Home %23 PrtScn F8 F2 F3 F4 F5 F6 F7 F9 近

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A continuous random variable X has the probability density function 0, hx - h, 3h-hx, 0, which can be graphed as f(x) h f(x) = x < 1 1≤x≤2 2≤ x ≤ 3 x > 3 2 3 X (a) Find h which makes f(x) a valid probability density function. (b) Find the cumulative distribution function F(x).