$y$ is standard normal random variable and $x=|y|$.
What will be the median of $x$?
$P (1 < x < 2)$?
$0.80$ quantile of $x$?
Standard normal variable median and quantile.
2
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probability
statistics
random-variables
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0i am completely blank in a – 2017-02-18
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0(a) median approx .67; (c) 80th percentile approx 1.28; (b) 0.2718 from normal tables. Use hint of @stud_iisc. – 2017-02-18
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0You seem to be simultaneously 'outsourcing' three fairly basic hwk problems. I fear that will soon lead to disaster in your course. Fine to work problems and check answers here. Sometimes even to get a nudge in the right direction, but cannot stay in 'completely blank' mode for long and survive. I've been teaching this stuff for almost 50 yrs and I don't see any good coming of this for you personally. Please read the chapter before you start hwk; don't just hope the right formula will magically jump off the page to rescue you. Almost never happens. And then there's exam time. Aargh! – 2017-02-18
1 Answers
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Hint:
You have to find $u$ such that $P(-\infty < x < u) = 0.5$. Here $u$ is the median of $x$.
$P (1 < x < 2) = P(-1
You have to find $v$ such that $P(-\infty < x < v) = 0.8$. Here $v$ is the $0.8$-quantile of $x$.
More hints as requested by @ernie:
$P(-\infty < x < u) = P(-\infty
Replace $u$ by $v$ and $0.5$ by $0.8$ in above.
Given $y \sim N(0,1)$, the above hints must be sufficient to find the end results.
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0Added more hints in the answer @ernie. – 2017-02-18
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0is the answer of a 0.674 – 2017-02-18
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0The median is ~0.674, yes. I was of some help. :) – 2017-02-18