2. Let f(y) be the density function and F(y) be the cumulative distribution func

Question

2. Let f(y) be the density function and F(y) be the cumulative distribution function (cdf) for a continuous random variable Y with support (-oo, oo). For each of the following indicate if it either always true (AT), never true (NT), or might be true (MBT), but not necessarily always true. MBT means there could be a continuous random variable Y with support (-oo, oo) where the statement is true, but it would not necessarily hold for all continuous random variables Y with support (-oo, oo). In a few of the questions the answer would change if the support were different There is only one question where the answer is MBT, so don't think too hard about the ones where your maybe there could be some unusual density function where it would be true. first answer is NT, but then you try to think that If you have a good understanding of what density functions and cdfs are, these question should be mostly easy (a) f(y) = (y) (b) F(y) = (y) (c) f(v)- F(u)du (d) F(v)- J f(u)du (e) f(y) >0 for all g

Explanation / Answer

a) AT

b) NT

c) AT

d) NT

e) AT

f) AT

g) NT

h) AT

i) NT

j) AT

k) NT

l) AT.

m) please clarify the range because, F(-infinity)=0,F(+infinity) 1,0<F(x)<1,for other cases.

n) apply same logic.

o) MBT.

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