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Question: suppose that 4is a sequence of independent identicallydistributed lld continuous...

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Suppose that (4)%!is a sequence of independent identicallydistributed (LLd.) continuous random variables. 4. Suppose that each ξǐ has a probability density function Pi (x)-| x 0, x<1 R. Let S2 a. Find a condition on α and a condition on β (as a function of α) which together make f(x) a b. Find conditions on a which guarantee that lim S, will converge in distribution to a standard c. Find the probability density function for Z-4. + ξ2 , where each ξ has density function probability density function. normal random variable. (Hint: what are the hypotheses of the central limit theorem?) To earn full credit, you must simplify your answer as much as 0, x<0 possible.
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