Recent content by quantum_2000

Crisp and clear! Reading your arguments was really instructive. Thank you again for sharing your thoughts Q

Thank you for your suggestions. I realized that I did not mention that x is constrained to be grater than k, this is why I observed a concave-convex function... my mistake. I could finally prove it. What I did was to look at the first order condition and show that it has a unique solution if...

True in general, and even the third derivative can help, but I do not see how it can be of help here. Please bring your ideas if you have any in this direction. --- I came up with a (sufficient) set of conditions to show q-concavity, but it's rather complex. I put it down in case it helps...

The first derivative of the function is -\phi(x)(x-k)+(1-\Phi(x)) the first term is always negative, the second always positive, so to prove quasi-concavity is would be sufficient to show that the first term increases in magnitude and the second decreases as x goes up (this would actually...

Homework Statement I need to prove that the function (1-\Phi(x))(x-k) is quasi-concave (i.e. first increasing and then decreasing), where \Phi is the cdf of the normal distribution and k is a positive constantHomework EquationsThe Attempt at a Solution I plotted the function and even tried...

So, in the end no one has a clue about it?

It is the integral of the pdf of a normal distribution times 1/t. With substitution I get the integral in the title where b is the mean of the distribution. So, if anyone has a solution to compute the integral of (1/t)*PDF(NormalDistribution(mu,sigma),t) from x>0 to +infinity, this would make me...

The reason why I need an analytical solution is that I need to be able to compute the integral in a single Excel cell for any given set of parameter values. So, say that a=20 b=50 and x=80, I need to compute in a single cell (that means without being able to compute partial results in any other...

Homework Statement I need to calculate the integral of (1/(at+b))e^(-t^2), that is, a negative quadratic exponential divided by a linear function at+b. I need to integrate between some positive x and +infinity.Homework Equations The Attempt at a Solution I could find the integral for b=0. In...