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By opening one store, the firm knows that the probability of high demand is 50%. The potential value gain to expand next year is thus 50%* (10M-8M)/1.1 = 0.91M. The value to open one store this year is 7.5M - 8M = -0.5. Thus the value of the real option to invest in one store, wait a year, and invest next year is 0.41M.
As another example, φ(1) = 1 since for n = 1 the only integer in the range from 1 to n is 1 itself, and gcd(1, 1) = 1. Euler's totient function is a multiplicative function , meaning that if two numbers m and n are relatively prime, then φ ( mn ) = φ ( m ) φ ( n ) .
The Boltzmann constant (kB or k) is the proportionality factor that relates the average relative thermal energy of particles in a gas with the thermodynamic temperature of the gas. [2] It occurs in the definitions of the kelvin (K) and the gas constant, and in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used in ...
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The 5% Value at Risk of a hypothetical profit-and-loss probability density function. Value at risk (VaR) is a measure of the risk of loss of investment/Capital. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day. VaR is typically used by firms and ...
Cross-validation includes resampling and sample splitting methods that use different portions of the data to test and train a model on different iterations. It is often used in settings where the goal is prediction, and one wants to estimate how accurately a predictive model will perform in practice.
A bijection with the sums to n is to replace 1 with 0 and 2 with 11. The number of binary strings of length n without an even number of consecutive 0 s or 1 s is 2F n. For example, out of the 16 binary strings of length 4, there are 2F 4 = 6 without an even number of consecutive 0 s or 1 s—they are 0001, 0111, 0101, 1000, 1010, 1110. There is ...
For example, using single-precision IEEE arithmetic, if x = −2 −149, then x/2 underflows to −0, and dividing 1 by this result produces 1/(x/2) = −∞. The exact result −2 150 is too large to represent as a single-precision number, so an infinity of the same sign is used instead to indicate overflow.