Question: Consider a sample space S and corresponding event space F. Suppose that P1 and P2 are both valid probability measures defined on F. Show that

Consider a sample space S and corresponding event space F. Suppose that P1

and P2 are both valid probability measures defined on F. Show that P defined

by

P(A) = (alpha)P1(A) + 2(beta)P2(A), for all A in F

is also a valid probability measure on F if alpha, beta>0 and alpha + beta= 1

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