From the given density function we find the distribution function,
![F_Y(y)=P(Y\le y)=\displaystyle\int_{-\infty}^y f_Y(t)\,\mathrm dt=\begin{cases}0&\text{for }y](https://tex.z-dn.net/?f=F_Y%28y%29%3DP%28Y%5Cle%20y%29%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5Ey%20f_Y%28t%29%5C%2C%5Cmathrm%20dt%3D%5Cbegin%7Bcases%7D0%26%5Ctext%7Bfor%20%7Dy%3C-1%5C%5C%5Cfrac%7By%5E3%2B1%7D2%26%5Ctext%7Bfor%20%7D-1%5Cle%20y%3C1%5C%5C1%26%5Ctext%7Bfor%20%7Dy%5Cge1%5Cend%7Bcases%7D)
(a)
![F_{U_1}(u_1)=P(U_1\le u_1)=P(3Y\le u_1)=P\left(Y\le\dfrac{u_1}3\right)=F_Y\left(\dfrac{u_1}3\right)](https://tex.z-dn.net/?f=F_%7BU_1%7D%28u_1%29%3DP%28U_1%5Cle%20u_1%29%3DP%283Y%5Cle%20u_1%29%3DP%5Cleft%28Y%5Cle%5Cdfrac%7Bu_1%7D3%5Cright%29%3DF_Y%5Cleft%28%5Cdfrac%7Bu_1%7D3%5Cright%29)
![\implies F_{U_1}(u_1)=\begin{cases}0&\text{for }u_1](https://tex.z-dn.net/?f=%5Cimplies%20F_%7BU_1%7D%28u_1%29%3D%5Cbegin%7Bcases%7D0%26%5Ctext%7Bfor%20%7Du_1%3C-3%5C%5C%5Cfrac%7B%5Cleft%28%5Cfrac%7B%7Bu_1%7D%7D3%5Cright%29%5E3%2B1%7D2%26%5Ctext%7Bfor%20%7D-3%5Cle%20u_1%3C3%5C%5C1%26%5Ctext%7Bfor%20%7Du_1%5Cge3%5Cend%7Bcases%7D)
![\implies f_{U_1}(u_1)=\begin{cases}\frac{{u_1}^2}{18}&\text{for }-3\le u_1\le3\\0&\text{otherwise}\end{cases}](https://tex.z-dn.net/?f=%5Cimplies%20f_%7BU_1%7D%28u_1%29%3D%5Cbegin%7Bcases%7D%5Cfrac%7B%7Bu_1%7D%5E2%7D%7B18%7D%26%5Ctext%7Bfor%20%7D-3%5Cle%20u_1%5Cle3%5C%5C0%26%5Ctext%7Botherwise%7D%5Cend%7Bcases%7D)
(b)
![F_{U_2}(u_2)=P(3-Y\le u_2)=P(Y\ge3-u_2)=1-P(Y](https://tex.z-dn.net/?f=F_%7BU_2%7D%28u_2%29%3DP%283-Y%5Cle%20u_2%29%3DP%28Y%5Cge3-u_2%29%3D1-P%28Y%3C3-u_2%29%3D1-F_Y%283-u_2%29)
![\implies F_{U_2}(u_2)=\begin{cases}0&\text{for }u_2](https://tex.z-dn.net/?f=%5Cimplies%20F_%7BU_2%7D%28u_2%29%3D%5Cbegin%7Bcases%7D0%26%5Ctext%7Bfor%20%7Du_2%3C2%5C%5C1-%5Cfrac%7B%283-u_2%29%5E3%2B1%7D2%26%5Ctext%7Bfor%20%7D2%5Cle%20u_2%3C4%5C%5C1%26%5Ctext%7Bfor%20%7Du_2%5Cge4%5Cend%7Bcases%7D)
![\implies f_{U_2}(u_2)=\begin{cases}\frac32(u_2-3)^2&\text{for }2\le u_2\le4\\0&\text{otherwise}\end{cases}](https://tex.z-dn.net/?f=%5Cimplies%20f_%7BU_2%7D%28u_2%29%3D%5Cbegin%7Bcases%7D%5Cfrac32%28u_2-3%29%5E2%26%5Ctext%7Bfor%20%7D2%5Cle%20u_2%5Cle4%5C%5C0%26%5Ctext%7Botherwise%7D%5Cend%7Bcases%7D)
(c)
![F_{U_3}(u_3)=P(Y^2\le u_3)=P(-\sqrt{u_3}\le Y\le\sqrt{u_3})=F_Y(\sqrt{u_3})-F_y(\sqrt{u_3})](https://tex.z-dn.net/?f=F_%7BU_3%7D%28u_3%29%3DP%28Y%5E2%5Cle%20u_3%29%3DP%28-%5Csqrt%7Bu_3%7D%5Cle%20Y%5Cle%5Csqrt%7Bu_3%7D%29%3DF_Y%28%5Csqrt%7Bu_3%7D%29-F_y%28%5Csqrt%7Bu_3%7D%29)
![\implies F_{U_3}(u_3)=\begin{cases}0&\text{for }u_3](https://tex.z-dn.net/?f=%5Cimplies%20F_%7BU_3%7D%28u_3%29%3D%5Cbegin%7Bcases%7D0%26%5Ctext%7Bfor%20%7Du_3%3C0%5C%5C%7Bu_3%7D%5E%7B3%2F2%7D%26%5Ctext%7Bfor%20%7D0%5Cle%20u_3%3C1%5C%5C1%26%5Ctext%7Bfor%20%7Du_3%5Cge1%5Cend%7Bcases%7D)
![\implies f_{U_3}(u_3}=\begin{cases}\frac32\sqrt u&\text{for }0\le u\le1\\0&\text{otherwise}\end{cases}](https://tex.z-dn.net/?f=%5Cimplies%20f_%7BU_3%7D%28u_3%7D%3D%5Cbegin%7Bcases%7D%5Cfrac32%5Csqrt%20u%26%5Ctext%7Bfor%20%7D0%5Cle%20u%5Cle1%5C%5C0%26%5Ctext%7Botherwise%7D%5Cend%7Bcases%7D)
Answer:
72 degrees
Step-by-step explanation:
Delta Math
Answer:
choice one
Step-by-step explanation:
fnjddjdjdjddjnddkkdd
Answer:
look down below
Step-by-step explanation:
We know that AB = DC, and BC = AD, ∠B = ∠D because they are given
So, ΔABC ≅ ΔCDA because of SAS congruency