Probability theory

ISE SUMMER PROJECT 2015 Probability, randomness, and chance should be central in any STEM pedagogical model. The concepts of randomness and chance play a very significant role in the essence of all sciences, and especially in the empirical sciences. Randomness is a critical component of biological modeling at many levels in a wide range of systems. The fundamental axioms of the quantum paradigm in physics are, by definition, essentially stochastic. Economics uses the randomness in human thought…

With different design of sampling probabilities, we can apply dropout to the learned metric to simulate the effect of L1 regularization. In particular, we introduce a data dependent dropout probability as Now, instead of perturbing Mt−1, we apply dropout to M’ t , i.e. the matrix after the gradient mapping. It is easy to verify that the expectation of the perturbed matrix Mˆ 0 is given…

After 30 s, the search mission is commenced. The updated probability map is transmitted to the service vehicles every 5 s by the host computer. The final configuration of planar position and the trajectories of all service vehicles for different time steps, 40 s, 90 s, 180 s are shown in Figure 6-3.1-1-c. The distribution density function based on the most updated probability maps are also shown in the figures. The color intensity is proportional to the value of distribution…

economists have not embraced a thinking logic such as his, which, by all means, seems incomparably more realistic now days than the respective one of the so-called orthodox economic theory. That being said, one would perhaps need to equally recognize that the majority of social experts, just like optimistic and pleasant theories. These very needs ordain a turning away from a reality filled with “negative” effects, fears and…

------------------------------------------------- A life insurance company wants to estimate their annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. What proportion of the plan recipients would receive payments beyond age 74? Round your result…

Ajay Devgan says, “By getting into distribution and production, I have actually widened my base” (Distribution Quotes, 2016). Distributions are all around us in the fields of programming, medical, the sciences in many of today colleges. For me, distributions occurred in the aspect of programming, childhood and motherhood. As a single mother with a son, distribution appears in many activities, such as college and taking care of my child. As a student in Trine University, statistics class has many…

results that are almost certain. The Law of Large Numbers is “A law expressing the fact that if a trial in which all outcomes are independent of each other and equally likely is repeated, then the relative frequency of each outcome approximates its probability with increasing accuracy as the number of repetitions becomes sufficiently large” is the definition given for law of large numbers (Law of Large Numbers). The application of weak law of large…

In our every day lives we are faced with risk; the possibility of losing something of value. This could include theft or re to property, sickness, disability or even death. As loss adverse as we are, we tend to set up mediums to prevent or recover from losses once incurred. One of these common mediums is insurance. Anderson and Brown (2005) denes insurance as an agreement where, for a stipulated payment called the premium, one party (the insurer) agrees to pay to the other (the policyholder or…

been a concern in the history of probability and statistics. In the act of tossing a coin, throwing a die to obtain a 6, either a machine work or fails, a student passing an exam or not and so on are events whose end results are either a yes or no, good or bad, present or absent, success or failure, as well as a win or loss. Generally, the history of probability and statistics, describe these activities to follow a Bernoulli distribution of the discrete probability distributions where an…

the links are Q=2mn. The rewiring algorithm includes Q steps, and at each step i, link i are chosen and rewired to a node randomly chosen over the graph with the intra-modular rewiring probability P, provided that multi-link and self-loops are prohibited. The probability P is the intra-modular rewiring probability in this modular network.…