SOLUTION: Let X be a continuous random variable whose values lie in [-1,1]. The probability density function is {{{f(x) = kx^2}}} What must the value of k be?

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Question 1136602: Let X be a continuous random variable whose values lie in [-1,1]. The probability density
function is f%28x%29+=+kx%5E2 What must the value of k be?
Answer by ikleyn(52869) About Me  (Show Source):
You can put this solution on YOUR website!
.

Integral of f(x) over the segment [-1,1] must be equal to 1.


Integral of f(x) over the segment [-1,1]  is  k%2A%28%281%2F3%29+-+%28-1%2F3%29%29 = %282%2Ak%29%2F3.


So, the equation to determine k is


    %282k%29%2F3 = 1

    2k = 3

    k = 3%2F2.    ANSWER