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Since the sample mean and variance are independent, and the sum of normally distributed variables is also normal, we get that: ^ + ˙ (+, + ()) Based on the above, standard confidence intervals for + can be constructed (using a Pivotal quantity) as: ^ + + And since confidence intervals are preserved for monotonic transformations, we get that
The sample mean of | W 200 | is μ = 56/5, and so 2(200)μ −2 ≈ 3.19 is within 0.05 of π. Another way to calculate π using probability is to start with a random walk , generated by a sequence of (fair) coin tosses: independent random variables X k such that X k ∈ {−1,1} with equal probabilities.
Section 4 of the Act contained the formula for determining which states or political subdivisions were covered by Section 5. [56] The majority opinion argued that the formula used to determine which jurisdictions required federal oversight or preclearance had not been updated to reflect current social conditions, including a decline in ...