Suppose Z ∼ N(0,1) and Y = e . (a) Find the cdf FY (a) and pdf fY (y) for Y . (For the CDF, the best you can do is write it in terms of Φ the standard normal cdf.) (b) We don’t have a formula for Φ(z) so we don’t have a formula for quantiles. So we have to write quantiles in terms of Φ−1. (i) Write the 0.33 quantile of Z in terms of Φ−1 (ii) Write the 0.9 quatntile of Y in terms of Φ−1. (iii) Find the median of Y .

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Suppose Z ∼ N(0,1) and Y = e .
(a) Find the cdf FY (a) and pdf fY (y) for Y . (For the CDF, the best you can do is write
it in terms of Φ the standard normal cdf.)
(b) We don’t have a formula for Φ(z) so we don’t have a formula for quantiles. So we have
to write quantiles in terms of Φ−1.
(i) Write the 0.33 quantile of Z in terms of Φ−1
(ii) Write the 0.9 quatntile of Y in terms of Φ−1.
(iii) Find the median of Y .

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