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Summary of statistical analysis 1. Normal distribution If a random variable can be described by a normal distribution, its density function is ( x − µ) 2 1 f ( x) = exp − 2σ 2 σ 2π Where σ is the standard deviation µ is the mean value f (x) is called the probability density function x is magnitude of the random variable The probability of a < x < b will be
(1)
( x − µ) 2 1 P (a < x < b) = ∫ f ( x)dx = ∫ exp − dx a σ 2π 2σ 2 a
b b
(2)
2. Standard normal distribution and the table The value of equation (2) is usually determined by a standard normal distribution table because the explicit solution is not available. The standard normal distribution is a normal distribution with σ =1 and µ =0. The probability density function of the standard normal distribution is µ2 1 f ( z) = exp − (3) 2π 2 Table 1 is the table of the standard normal (z) distribution, which is the same as table in page 50 of the textbook. The table...

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