- #1
kingwinner
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Q: Given f(x) = cx + (c^2)(x^2), 0<x<1.
What is c such that the above is a proper probability density function?
Solution:
1
∫ f(x) dx = 1
0
=> 2(c^2) + 3c - 6 =0
=> c= (-3 + sqrt57) / 4 or c= (-3 - sqrt57) / 4
=> Answer: c= (-3 + sqrt57) / 4 (the second one rejected)
======================================
Now, what is the reason of rejecting c= (-3 - sqrt57) / 4 ?
Also, in which step is this extraneous solution produced and why is it produced?
Thanks for explaining!
What is c such that the above is a proper probability density function?
Solution:
1
∫ f(x) dx = 1
0
=> 2(c^2) + 3c - 6 =0
=> c= (-3 + sqrt57) / 4 or c= (-3 - sqrt57) / 4
=> Answer: c= (-3 + sqrt57) / 4 (the second one rejected)
======================================
Now, what is the reason of rejecting c= (-3 - sqrt57) / 4 ?
Also, in which step is this extraneous solution produced and why is it produced?
Thanks for explaining!