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How do you find the value of 'k' in this probability density function?
This is the question that I have:
X is a continuous random variable having the probability density function
f(x) = k/x for 1≤x≤ 9
f(x) = 0 elsewhere
where k is a constant.
Giving your answers to 3 significant figures where appropriate, find the value of k
btw i got ended up with klnx=1, but I'm not sure what to do from there
Thanks Wil, but does this make k a constant? How can I find out the median of X if I'm left with k=1/ln9?
1 Answer
- Will HLv 77 years agoFavorite Answer
9
∫ k/x dx
1
= kln(9)
and
kln(9) = 1
k = 1/ln(9)
k = 0.455
EDIT
See here
http://math.ucsd.edu/~wgarner/reference/math10c_su...
The median is the value for which P(X > x) = 1/2 and P(X < x) = 1/2. Integrate to find the CDF and set it equal to 1/2.
f(x) = kln(x) = 1/2
ln(x) = 1/[2k]
ln(x) = 1/[2*0.455]
ln(x) =1.1 approx
x = e^(1.1) approx
x = 3 approx.
