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 February 2nd, 2016, 12:45 PM #1 Newbie   Joined: Feb 2016 From: Michigan Posts: 2 Thanks: 0 Random variable with continuous distribution Hello, I'm stuck with following problem: Random variable X with the continuous distribution for some arbitrary constant a > 0: $\displaystyle p(x) = 3/4a³(a² - x²)$ if |x| < a otherwise 0 i. Draw the distribution ii. Show that p(x) is a valid distribution Some hints how to get started with the problem would be appreciated!
 February 2nd, 2016, 02:49 PM #2 Math Team   Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 Can you clarify $p(x)$? Is it $\dfrac{3}{4a^2(a^2 - x^2)}$, $\dfrac{3}{4a^2}(a^2 - x^2)$, $\dfrac{3}{4}a^2(a^2 - x^2)$? A small latex tip; If you want to make your exponents more visible, use ^n. For example, the code a^n will give $a^n$. Thanks from Prob
February 2nd, 2016, 04:41 PM   #3
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 Originally Posted by Prob Hello, I'm stuck with following problem: Random variable X with the continuous distribution for some arbitrary constant a > 0: $\displaystyle p(x) = 3/4a³(a² - x²)$ if |x| < a otherwise 0 i. Draw the distribution ii. Show that p(x) is a valid distribution Some hints how to get started with the problem would be appreciated!
For i), just substitute, say, a = 1 and plot some points. (Or use use the first and second derivative tests - your choice lol.)

For ii), you have to show that the area under the curve = 1, i.e. integrate p(x) from -a to a.

 February 2nd, 2016, 09:25 PM #4 Newbie   Joined: Feb 2016 From: Michigan Posts: 2 Thanks: 0 p(x) is: $\displaystyle p(x) = \frac{3}{4a^{3}}(a^2-x^2)$

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