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8

I do not give an answer to your question(s) (yet), but hand over a different approach. Probability corresponding with sum $5$ is $\frac{4}{36}$ and probability corresponding with sum $7$ is $\frac{6}{36}$. Neglecting the other outcomes we find a probability $\frac{4}{10}$ for sum $5$ and $\frac{6}{10}$ for sum $7$. If on base of these probabilities a ...

6

A simple approach would be to "split the world" into two events: The event in which a sum of $5$ appears before a sum of $7$ The event in which a sum of $7$ appears before a sum of $5$ Since these are complementary events, the probability that either one of them will occur is $1$. Now, the probability of a sum of $5$ is $\color\red{1/9}$, and the ...

4

In your first approach the events are not disjoint: For example the event where the first two rolls are $5$ is contained in both of the first two events. In the second approach the events are disjoint and their union is the event that $5$ appeared before $7$, so this is the way to go. Indidentally, if we can assume the throws are all independent, a neat ...

3

Your process has random samples $X_t$ at times $t=0,1,2,\ldots$ from a continuous state space $[0,4]$. The state $x = 4$ is absorbing and reachable from every transient state, so this is an absorbing Markov chain. I'm going to restate the specific rules of the random process for the sake of definiteness. I believe my interpretation is consistent with the ...

2

$P'(\phi)=125-30\phi=0 \quad \Rightarrow \phi=25/6$ Since $P'(\phi)>0$ for $\phi<25/6$ and $P'(\phi)<0$ for $\phi>25/6$ We have the maximum at $\phi=25/6$ But I assume that we cannot have a partial number of rebates so since $25/6$ is closer to $4$ than $5$, the optimal number is \400$of rebate. Sanity Check:$P(4)=(1500-400)(1+.6)=1760$... 1 Joffan is definitely on the right track. The different time intervals of his schedule form the vertices of a graph. Add a source linked to all vertices, and link all vertices to a sink. Then, add an edge between two vertices$u$and$v$if they correspond to two possible successive flights (i.e., the arrival city of$u$and the departure city of$v$are ... 1 First thing I would do - apart from (as your comment says) finding out how long a relocation flight takes over the three routes, and what the turn-around time is between flights - is lay out the schedule on a time basis to get some ideas of what the key items are to capture in your data model. You can already see there's another data issue with the last ... 1 You can try to look into Mathematical Tools for Understanding Infectious Disease Dynamics:, however, you do need quite good mathematical background to start reading it. This book includes careful derivation (and drawbacks) of the classical SIR model, and treats branching processes from scratch. It does include statistical aspects, but I do not think it has ... 1 You may want to order the elements of$F$into a given vector$\mathbf{f} \in F^n$, where$F^n = F \times F \times ... \times Fn$times (that is, if the elements of$F\$ are distinct; otherwise you are using a multiset). This will allow for a reasonable input representation for a vector-valued function. To indicate that you are assembling a vector, you ...

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