The predefined product structure is used as the predetermined condition, and the up consistency rule is proposed as the preprocessing step. The conditional probability is extended as the core algorithm. The evaluation method of judgment threshold is designed based on the maximum likelihood estimation. ...
(d) How many times would you need to roll the die in order to have probability greater than 0.5 of getting at least one run of three consecutive 3’s? 3. Check part of the previous question by programing and running a simulation to approximate the probability of at least one run of th...
Product rule The product rule gives us a straightforward method to find the derivative of the product of two functions. Let's take two arbitrary functions, f(x) and g(x), and multiply them. So, . The derivative is . Let's explore this in more detail to understand how this works. Hav...
T ÒE ∪ FÓ is the probability that at least one of the two events Eß F occurs. This was reviewed in Section 0, where a similar rule was described for counting the number of elements in E ∪ F . For the union of three sets we have T ÒE ∪ F ∪ GÓ œ T ÒEÓ...
We omit a proof of Proposition 3.3 as the results follow directly from (13) and elementary rules of differentiation like the chain rule. While the expressions in Proposition 3.3 appear complicated at first sight, it is important to realize that they can be evaluated very efficiently. Next we ...
Conditional on a HMDA loan being sold, a greater share was purchased by GSEs following the announcement of the HUD rule in 2000. The blue dashed line captures the prevalence of differentiated loans in Prime MBS deals (values correspond to the y-axis on the right). Notably, the figure ...
Conditional probability Life is a series of events, each carrying its own uncertainties. Probability offers a mathematical framework to navigate and manage these uncertainties. Because life is inherentlyinterconnected, it becomes essential to explore therelationships between events and their joint probabiliti...
To rule out such a scenario, we restrict attention to the range of θ that guarantees a positive margin for the supply chain. This range is defined by the upper bound θ > 0, which is the unique solution to the equation c (θ) /θ = v0. (It can be shown that such a solution ...
where A and B represent the item sets (topic words), A⇒Bdenote an association rule, greater than minimal support value S, and S represents the ratio of all topics that include both topic words A and B, which denoteP(A∪ B). If S is smaller, it means that the relationship between...
Lemma 1 indicates that Assumption 1 is not restrictive in the sense that it does not rule out any equilibrium that is in the interior of the strategy space. More importantly, because of this result, we are able to develop an algorithm searching for all pure strategy Nash equilibria over the...