a. The marginal densities
![f_X(x)=\displaystyle\int_0^1(x+y)\,\mathrm dy=x+\frac12](https://tex.z-dn.net/?f=f_X%28x%29%3D%5Cdisplaystyle%5Cint_0%5E1%28x%2By%29%5C%2C%5Cmathrm%20dy%3Dx%2B%5Cfrac12)
and
![f_Y(y)=\displaystyle\int_0^1(x+y)\,\mathrm dx=y+\frac12](https://tex.z-dn.net/?f=f_Y%28y%29%3D%5Cdisplaystyle%5Cint_0%5E1%28x%2By%29%5C%2C%5Cmathrm%20dx%3Dy%2B%5Cfrac12)
b. This can be obtained by integrating the joint density over [0.25, 1] x [0.5, 1]:
![P(X>0.25,Y>0.5)=\displaystyle\int_{1/4}^1\int_{1/2}^1(x+y)\,\mathrm dx\,\mathrm dy=\frac{33}{64}](https://tex.z-dn.net/?f=P%28X%3E0.25%2CY%3E0.5%29%3D%5Cdisplaystyle%5Cint_%7B1%2F4%7D%5E1%5Cint_%7B1%2F2%7D%5E1%28x%2By%29%5C%2C%5Cmathrm%20dx%5C%2C%5Cmathrm%20dy%3D%5Cfrac%7B33%7D%7B64%7D)
Answer:
Step-by-step explanation:
Add the segment LX, parallel to QP.
Recall the properties of midsegment:
- Midsegment is parallel to side,
- Midsegment is half the length of the parallel side.
We have:
- Since QL = LR, the point L is midpoint of Q,
- Since PN = NL, the point N is midpoint of PL,
- Since LX is parallel to QP, LX is midsegment of ΔPRQ.
Find the length of LX:
Since QP ║ LX ║ NM, the segment NM is the midsegment of ΔPLX.
Find the length of NM:
6’000’000.005
Work:
6*1000000 + 5/1000
Answer:
2n+17
Step-by-step explanation:
Answer:
For 9., the answer is x = -6
For 10., the answer is x = 6
For 11., the answer is x = -7
For 12., the answer is x = -6