a.
is a joint density function if its integral over the given support is 1:


so the answer is yes.
b. We should first find the density of the marginal distribution,
:


Then

or about 0.2019.
For the other probability, we can use the joint PDF directly:

which is about 0.7326.
c. We already know the PDF for
, so we just integrate:
![E[Y]=\displaystyle\int_{-\infty}^\infty y\,f_Y(y)\,\mathrm dy=\frac15\int_0^\infty ye^{-y/5}\,\mathrm dy=\boxed5](https://tex.z-dn.net/?f=E%5BY%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20y%5C%2Cf_Y%28y%29%5C%2C%5Cmathrm%20dy%3D%5Cfrac15%5Cint_0%5E%5Cinfty%20ye%5E%7B-y%2F5%7D%5C%2C%5Cmathrm%20dy%3D%5Cboxed5)
Answer:
a. A is disjoint to B
b. A is subset of B
c. A -B
d. A union B complement
e. A intersection B complement
f. B-A complement
The slope of a line in form ax+by=c is -a/b
the yint of the line is c/b
so
-6x-5y=15
slope=-(-6)/-5=6/-5=-6/5
yint is 15/-5=-15/5=-3
slope=-6/5
yint is -3
or you could just do slope intercept and solve for y
y=mx+b
m=slope
b=yintercept
slope=-6/5
yint is -3
Answer:
68
Step-by-step explanation:
the brackets make the 3 positive