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June 20th, 2017, 02:06 PM  #1 
Member Joined: Apr 2017 From: PA Posts: 45 Thanks: 0  Find a, b, and c if µ(X) = 0, σ^2(X) = 1/15
Let X be a random variable with range [−1,1] and density function f = ax^2 + bx + c if x < 1 and 0 otherwise. (d) Find a, b, and c if µ(X) = 0, σ^2(X) = 1/15, and sketch the graph of fX(x) . for this, I thought about taking the definite integral of ∫(ax^2+bx+c)dx from 1 to 1, to get (a/3)+(b/2)+c+(a/3)+(b/2) to eventually get ((2a)/3)+2c=0. Then, I thought about getting a by itself to get a=3c, and for b, since they canceled, I would have to say that B may not exist. Also, as for C, I got (a/3), how should you find a, b, and c? 
June 20th, 2017, 10:41 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,975 Thanks: 1026 
you have 3 equations for the 3 unknowns $f(x) = a x^2 + b x + c$ $\displaystyle \int \limits_{1}^1 ~f(x) ~dx = 1$ $\displaystyle \int \limits_{1}^1 ~xf(x) ~dx = 0$ $\displaystyle \int \limits_{1}^1 ~x^2 f(x) ~dx = \dfrac{1}{15}$ these should be relatively straightforward to expand and solve. yell back if you need further assistance. 

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1 or 15, µx, find, σ2x 
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