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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online