The Choquet integral is a well known aggregation function that generalizes several other well known functions. For example, appropriate parameterizations r
For the cases where T is an exponential distribution or a uniform distribution, we characterize the threshold of the equilibrium control as the unique root of a simple equation. The article is organized as follows: in Sect. 2, we introduce the game model in more detail. For deriving a candi...
the two graphs were pretty much on top of each other. That’s not a proof that is the answer, of course, but it’s certainly a good indicator. I didn’t have the same luck with the other sum; I could graph it but wasn’t able to just guess what the curve could be. John ...
In accordance with the constant-variation-formula for discrete-time and discrete-space model, Banach contracting mapping principle, the method of proof by contradiction and stochastic calculus, we also obtain the existence of a unique bounded almost periodic sequence for the discrete model, which is ...
Proof: We can write W=E[X~|Y]=E[X−X^M|Y]=E[X|Y]−E[X^M|Y]=X^M−E[X^M|Y]=X^M−X^M=0.W=E[X~|Y]=E[X−X^M|Y]=E[X|Y]−E[X^M|Y]=X^M−E[X^M|Y]=X^M−X^M=0. The last line resulted because X^MX^M is a function of YY, so E[...
Think of the quantum state as encoding some information about your system. That is to say some quantum version of a probability distribution defined on a vector space (Hilbert space). What do we want of a meaningful probability distribution? First it must be always normalized so that mutually...
In this article, the error term of the mean value theorem for binary Egyptian fractions is studied. An error term of prime number theorem type is obtained unconditionally. Under Riemann hypothesis, a power saving can be obtained. The mean value in short interval is also considered. Keywords: ...
Use the MGF of the Geom(p) distribution to give another proof that the mean of this distribution is q / p and the variance is q / p 2 , with q = 1 ? p . Compute E [X^4] for X \sim N(0, 1), and then derive mean and variance of \chi_n...
Answer to: Under what conditions, if any, is it not correct to assume that the sampling distribution of the sample mean is approximately normally...
Intuitively, it gives a probability distribution on the indices \(i=1,\dots ,|{\mathcal {A}}|\) which has higher values on indices whose corresponding values are closer to be a minimum. In particular, the elements of \(\min \{i=1,\dots ,|{\mathcal {A}}| : z_i = {{\,\mat...