There are many mathematical formulations of the clt

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Unformatted text preview: tribution with µ = 0 and σ 2 = 1. It is also called the N (0, 1) distribution. The CDF of the N (0, 1) distribution is traditionally denoted by the letter Φ (Phi): u 1 v2 √ exp − Φ(u) = dv, 2 2π −∞ and the complementary CDF of the N (0, 1) distribution is traditionally denoted by the letter Q, (at least in much of the systems engineering literature). So ∞ Q(u) = u 1 v2 √ exp − 2 2π dv = 1 − Φ(u) = Φ(−u). Since Q(u) = 1 − Φ(u) = Φ(−u), any probabilities we can express using the Q function we can also express using the Φ function. There is no hard and fast rule for whether to use the Φ function or the 90 CHAPTER 3. CONTINUOUS-TYPE RANDOM VARIABLES Q function, but typically we use Q(u) for values of u that are larger than three or four, and Φ(u) for smaller positive values of u. When we deal with probabilities that are close to one it is usually more convenient to represent them as one minus something, for example writing 1 − 8.5 × 10−6 instead of 0....
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.

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