13. suppose that form a random sample from a distribution for which the p. d.f. is f (x|θ ), where the value of the parameter θ belongs to a given parameter space ? . suppose that t = r() and t ? = r? () are two statistics such that t ? is a one-to-one function of t ; that is, the value of t ? can be determined from the value of t without knowing the values of , and the value of t can be determined from the value of t ? without knowing the values of . show that t ? is a sufficient statistic for θ if and only if t is a sufficient statistic for θ.

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85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560

because that’s us why