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Unformatted text preview: 36226 Summer 2010Homework 6Due July 211. Suppose thatXis distributed N(0,2).(a) What is the distribution ofX2/2?(b) Using the pivotal quantity from part (a), find a 95% confidence interval for2of the forma <2< b.(c) Find another 95% CI for2, this time of the forma < 2<.(d) Find another 95% CI for2, this time of the form 0< 2< b.2. SupposeX1,...,Xnare a random sample from a Normal(,1) distribution.(a) Find an interval based on the distribution ofXwhich will contain90% of the time.(b) Comment on how this interval varies as the sample size increases.3.(a) SupposeXis a random sample from a Uniform(0,) distribution. LetY=FX(x), whereFX(x) =P(Xx) =x. ThenYis a random variable; it is just a transformation of the random variableX. ComputeP(Yt) =P(Xt).(b) What can you conclude about the distribution ofY=FX(x) ifXU(0,)?(c) Now, supposeXis a random sample from an Exponential() distribution. LetY=FX(x). RecallthatFX(x) = 1ex, as was shown in class. Compute, as was shown in class....
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 Summer '09

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