Isye 2027

# For n 1000 002 and p 05 this is equal to 21265

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Unformatted text preview: ve integers. For example, P {X ≤ 2.5} = 0.6778 and P {X ≤ 2.5} = 0.6537. 94 CHAPTER 3. CONTINUOUS-TYPE RANDOM VARIABLES Since X is an integer-valued random variable, P {X ≤ 2.5} = P {X ≤ 2}. Therefore, we have: P {X ≤ 2} = P {X ≤ 2.5} ≈ P {X ≤ 2.5}. So, P {X ≤ 2.5} is a fairly good approximation to P {X ≤ 2}. In particular, it is a better approximation than P {X ≤ 2} is–in this case P {X ≤ 2} = 0.5. In general, when X is an integer-valued random variable, the Gaussian approximation with the continuity correction is: P {X ≤ k } ≈ P {X ≤ k + 0.5} P {X ≥ k } ≈ P {X ≥ k − 0.5}. (Gaussian approximation with continuity correction) The example just given shows that, with the continuity correction, the Gaussian approximation is fairly accurate even for small values of n. The approximation improves as n increases. The CDF of X and X are shown in Figure 3.12 in case X has the binomial distribution with parameters n = 30 and p = 0.2. Figure 3.12: The CDF of a...
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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 Tech.

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