Kennedy and Gentle (1980) provide the following algorithm for generating a beta distribution Generate U1 and U2two independent observations from the U 0, 1 distribution For 0 and 0 denote V1 U 1 and V2 U 2 According to the Accept Reject algorithm, let X V1 (V1 V2) if V1 V2 1 otherwise, start the procedure again (i) Determine the distribution of a random variable X (ii) Use this algorithm to generate a random sample of size 3 from BETA(0 732, 1 281)

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Question: Kennedy and Gentle (1980) provide the following algorithm for generating a beta distribution: Generate U1 and U2two independent observations from the U[0, 1] distribution. For

Kennedy and Gentle (1980) provide the following algorithm for generating a beta distribution: Generate U1 and U2—two independent observations from the U[0, 1]

distribution. For α > 0 and β > 0 denote V1 = U α

1 and V2 = Uβ

2 . According to the Accept/Reject algorithm, let X = V1/(V1 + V2) if V1 + V2 ≤ 1; otherwise, start the procedure again. (i) Determine the distribution of a random variable X. (ii) Use this algorithm to generate a random sample of size 3 from BETA(0.732, 1.281).

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