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Relation between exponential and beta distribution

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Suppose that X_i has an exponential distribution with a parameter lamda_i > 0. How do a series of exponential distribution functions with distinctive pairwise of random variable X and lamda (ie X_1 and lamda_1, X_2 and lamda_2,..., X_n and lamda_n) be transformed into a beta distribution function?

Note: X_i are independent identically distributed values. Also we have noted the lambda values has a steadily and small increasing trend so it is not totally independent.

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Solution Summary

This solution shows the steps to determining the relationship between the exponential and beta distribution functions.

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