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Unformatted text preview: tribution with α = 2 and β = 3. p.d.f. of Beta Distribution with alpha = 2 and beta = 3 y f(y) 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.5 1.0 1.5 Distribution of Beta Distribution with alpha = 2 and beta = 3 y F(y) 0.0 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 • The theoretical mean of the beta distribution is μ = E ( Y ) = α α + β • The variance of the beta distribution is σ 2 = V ( Y ) = αβ ( α + β ) 2 ( α + β + 1) Working with the beta distribution in R. To ±nd the probability P ( Y ≤ y ) the command in R is pbeta(y,alpha,beta) 1 To fnd the value oF y so that P ( Y ≤ y ) = p the command in R is qbeta(p,alpha,beta) To generate observations From a beta distribution the command in R is rbeta(numobs,alpha,beta) where numobs is the number oF observations you would like to generate. 2...
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- Spring '08
- Probability theory, Beta distribution