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  1. Jul 17, 2024 · The probability that a point lies inside some region inside the square is equal to the area of that region. Consider the equation \(x^2 + ax + b = 0\). Compute the probability when the roots of this equation are real. (Hint: Compute the area of the region \(a^2 \geq 4b\) and bounded by the unit square.) 4.

  2. Jul 17, 2024 · Various probability distributions of importance in physics are discussed in this chapter. Both discrete as well as continuous random variables are described. Among the discrete ones, the binomial distribution, the related random walk, and the Poisson distribution are discussed. Among the continuous distributions, the most important, namely, the ...

  3. 4 hours ago · Arizona Sonoran Copper Company Inc. , releases its updated Mineral Resource Estimate for the Cactus brownfield copper project, located 45 miles south of Phoenix, Arizona .

  4. 23 hours ago · In probability theory, events are categorized as dependent or independent based on their relationship to each other. Independent events, such as flipping a coin and rolling a die, have outcomes that do not affect each other. The probability of both independent events occurring is the product of their individual probabilities. On the other hand, dependent