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1d
comment Sufficient conditions for monotonicity with probability distributions
No, a negative $\delta$ reverses everything: larger $n$ reduces $A_n$.
1d
answered Assumptions of a probability distribution
1d
comment Derivatives defined on a discrete state space
Well this is standard economics; deriving demand functions should be explained in every microeconomics textbook. The above decision problem seems a bit macroish, so you might also find something useful in macroeconomics textbooks, typically with infinitely many future periods and a discount factor ("infinite horizon decision problem") instead of just two periods as in your case. Acemoglu: "Introduction to modern economic growth", ch. 5 and others work with suchs problems.
2d
comment Derivatives defined on a discrete state space
Not necessarily: typically the demand function is defined/constructed for all $\omega\in[0,\bar{\omega}]$, where $\bar{\omega}$ is the largest possible realization of $\omega$. So the function can be continuous in $\omega$ (Berge's maximum theorem guarantees the demand function will be upper hemi-continuous in $\omega$). The demand function is like a plan: it gives you a consumption level for each value $\omega\in[0,\bar{\omega}]$. But since not every value in that set actually realizes, it is true that the actual consumption may be discontinuous, because wealth is discrete.
2d
comment Derivatives defined on a discrete state space
Here's how I think it works: at some point $t$, the decision maker (DM) has wealth $\omega$. This is the state variable. Wealth may be exogenous or evolves according to some process. At time $t$, the DM knows $\omega$, and he chooses consumption this period and saves the rest for next period. Next period, there is some uncertainty (over $\omega_{t+1}$?), hence the E-operator. So the demand/consumption function is a mapping $C:[0,\omega]\to[0,\omega]$ which tells you which part of wealth is consumed now and which is saved. I think just the the $\omega$ process over time is discrete.
2d
answered Derivatives defined on a discrete state space
Dec
13
comment How can I infer order from partially ordered discrete sequences?
You could use some regression or machine learning techniques to estimate the probability that user $i$ has defining action $a$ given action history (prior to last session) $H_i=(a_{i,t=1},a_{i,t=2},..)$ and a set of possible defining actions $X_i$ (all actions taken in last session, where order is not observable). That is, you estmate $P(a=x\in X_i|H_i)$. You can do this by using the data where only one action is taken in the last session (you know the defining action), and by assuming that behavior between those with identifiable defining action and with non-identifiable action is similar.
Dec
13
comment How to estimate the variance of several populations when every population mean and variance is different?
On your comment: I think you are right, pooled variance is like a mean variance rather than the variance of the pooled population.
Dec
12
comment Optimal value of decision variable leads to inconsistency
Since the variable wrt optimization also influences the integration border, you must use Leibniz integral rule: en.wikipedia.org/wiki/Leibniz_integral_rule - there should be some $-0.75/A^2$ term. Also, are you sure that your problem is globally concave?
Dec
12
comment Assigning value in a marketplace
But if buyers and sellers are heterogeneous, then an additional buyer may be valuable even if there are more buyers than sellers, because he might replace another buyer (and create more value)? Also, your problem description is a bit unspecific. How exactly is value created in this market? What is the goal - maximize trade?
Dec
11
reviewed Approve Surface integral of the union of two lines in 3D space
Dec
11
reviewed Approve Expressing $\sin\theta$ and $\cos\theta$ in terms of $\tan(\theta/2)$
Dec
11
reviewed Approve Applying math knowledge
Dec
10
awarded  Caucus
Dec
6
reviewed Approve Can an explicit formula be found for a bijection $f \colon \mathbb{N} \to \mathbb{Q}$?
Dec
1
revised Does this equation have a solution?
added 1 character in body; edited title
Dec
1
comment Does this equation have a solution?
Certainly not if $C>1$.
Dec
1
answered Does the concept of “dynamic average” makes any sense?
Dec
1
comment Does the concept of “dynamic average” makes any sense?
Why is the average not 2.5 on those two days? Also, shouldn't you start summing at $i=1$ in the discrete case?
Dec
1
revised Does the concept of “dynamic average” makes any sense?
English improvement