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- Show that the caplet and floorlet values obtained in problems 24.2 and 24.3 satisfy caplet–floorlet parity Hint: Accounts & FinanceCaplet is a type of call option that is based on interest rates. Caplet is used to set limits the cost for the increasing interest rates for the cooperation so governments, where..
- Show that the chemical potential of an ideal gas is proportional to the logarithm Hint: EconomicsIn thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction ..
- Show that the coefficient of performance between reservoirs at absolute temperatures Hint: StatisticsCorrelation coefficients : They, between the two variables, are used to measure how strong the relationship. Also, there are several types of correlation coefficient in which the most popula..
- Show that the curve is a regular elliptic curve Hint: MathematicsElliptic curve cryptography (ECC): It is an approach to public-key cryptography which, over finite fields, is based on the algebraic structure of elliptic curves. Also, these Elliptic curve..
- Show that the distribution of Z3 as an increment of Brownian motion Hint: StatisticsBrownian motion is also called as the Brownian movement. It is any of the several physical phenomena where most quantity is constantly under the small, random fluctuations. Basically, it is ..
- Show that the distribution you found in Your Turn 8b is the one that minimizes Hint: ScienceAnalogy is a cognitive process of transferring information or meaning from a particular subject to another, or a linguistic expression corresponding to such a process. In a narrower sense, anal..
- Show that the expected value and variance of Y are Hint: StatisticsVariance, estimation, and bias are important factors in statistical operations. The variance shows how far the estimated averages are from the expected values. Bias helps one know if a value..
- Show that the following function g(w) is convex Hint: Statistics"(a) To show that g(w) is convex, we need to show that its second derivative is non-negative for all w ∈ Rd.Let's compute the second derivative of g(w):∇^2 g(w) = ∇^2(1/m ∑(yi - w^T xi)^2)= ..
- Show that the Fourier transform of the rectangular window is Hint: MathematicsA Fourier transform is a mathematical transform that decomposes functions depending on space or time into functions depending on spatial frequency or temporal frequency. An example applicat..
- Show that the integral on the left-hand side, r Hint: MathematicsAn integral is a mathematical notion that explains displacement, area, volume, and other ideas that come from the combination of infinitesimal data. Integration is the term used to describe..
- Show that the jth element of the LSE of β is equivalent to the LSE of the coefficient Hint: StatisticsLSE: y - y = (r xy s y / s x)(x - x), solve for a^ and b^. The equation on the previous line is the point-slope form of the regression equation: The point is (x, y), The slope is r xy s y / ..
- Show that the l = 0 energy levels of a three-dimensional square well Hint: Science"(a) To find the energy levels of a three-dimensional square well with angular momentum quantum number l = 0, we need to solve the Schrödinger equation for the radial part of the wavefunction. ..
- Show that the likelihood function is proportional to Hint: StatisticsHow likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn ou..
- Show that the likelihood function of n observed random sample times-to-failure Hint: StatisticsProbability distribution: It shows the expected outcomes of the possible values for a given data generating process, and also comes in many shapes with certain different characteristics, i.e..
- Show that the Log Likelihood function for m data points can be written as Hint: ManagementLogistic regression is a statistical model, to model a binary dependent variable, which in its basic form uses a logistic function. Logistic regression, in regression analysis, is the estima..