if X is a continuous random variable defined as:
f(x) = {
1/16x + 1/4, -4 <= x <= 0
-1/16x + 14, 0 <= x <= 4
}
a) what is the 0.8 quantile?
b) 45th percentile?
I know the basic premise of the question, but being defined in 2 parts is what eludes me.
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if X is a continuous random variable defined as:
f(x) = {
1/16x + 1/4, -4 <= x <= 0
-1/16x + 14, 0 <= x <= 4
}
a) what is the 0.8 quantile?
b) 45th percentile?
I know the basic premise of the question, but being defined in 2 parts is what eludes me.
Lets assume f is the density.Quote:
Originally Posted by scorpion007
a) The 0.8 quantile is y such that p(x<y)=0.8, or:
int(-4, y) f(x) dx=0.8.
Now we know that int(-4,0) f(x) dx=0.5, so we want y such that:
int(0,y) f(x) dx=int(0,y) {-1/16x + 14} dx =0.3
b) same as befor except that 0.8 is replaced by 0.45, also as 0.45<0.5
we are on the other bit of the definition so:
The 45th percentile is the 0.45 quantile so we seek a y such that p(x<y)=0.45, or:
int(-4, y) f(x) dx=0.45.
or
int(-4,y) f(x) dx=int(-4,y) {1/16x + 14} dx =0.45
RonL