Answer:
a) c=3/4
b) for -1<x<1
F(x) = (3/4) ( x + (2-x^3)/3 )
c)
E(x)=0
Var(x) = 1/5
Step-by-step explanation:
Hi!
a)
In order to f(x) be a probability density function it must be normalized, which means that its integral must be equal to 1:
Since f(x) is zero for x>1 and x<-1
Therefore:
c=3/4
b)
The cumulative distribution fucntion F(x) can be obtained integrating f(x) from -∞ to x:
Since f(x) = 0 for x<-1
F(x) = 0 for x<-1
for -1<x<1:
for x>1
F(x)=1
c)
The mean E(x) can be found integrating xf(x)
We can easily infer that the mean must be zero, since f(x) is an even function and thus xf(x) is an odd function integrated in a simetric interval:
E(x) = 0
The variance of x, Var(x), can be evaluated integrating (x-E(x))^2f(x), since E(x)=0:
Since c=3/4
Var(x) = 1/5
Answer:
It's asking for a reflection. The point D is 5 points lower than the line, so the plot dot should be 5 points higher than the line, right above the other D point. Think of the line as a mirror.
The red dot in the attached image is the answer.
