We obtain the joint PMF directly from the joint MGF:
![\implies\mathrm{Pr}[X=x,Y=y]=\begin{cases}0.1&\text{for }x=y=0\\0.2&\text{for }x=1,y=0\\0.3&\text{for }x=0,y=1\\0.4&\text{for }x=y=1\\0&\text{otherwise}\end{cases}](https://tex.z-dn.net/?f=%5Cimplies%5Cmathrm%7BPr%7D%5BX%3Dx%2CY%3Dy%5D%3D%5Cbegin%7Bcases%7D0.1%26%5Ctext%7Bfor%20%7Dx%3Dy%3D0%5C%5C0.2%26%5Ctext%7Bfor%20%7Dx%3D1%2Cy%3D0%5C%5C0.3%26%5Ctext%7Bfor%20%7Dx%3D0%2Cy%3D1%5C%5C0.4%26%5Ctext%7Bfor%20%7Dx%3Dy%3D1%5C%5C0%26%5Ctext%7Botherwise%7D%5Cend%7Bcases%7D)
Then
![\mathrm{Pr}[X=Y]=\mathrm{Pr}[X=Y=0]+\mathrm{Pr}[X=Y=1]=0.1+0.4=\boxed{0.5}](https://tex.z-dn.net/?f=%5Cmathrm%7BPr%7D%5BX%3DY%5D%3D%5Cmathrm%7BPr%7D%5BX%3DY%3D0%5D%2B%5Cmathrm%7BPr%7D%5BX%3DY%3D1%5D%3D0.1%2B0.4%3D%5Cboxed%7B0.5%7D)
When the value of x is 3, evaluate;
Substitute for the value of x into the parenthesis;
ANSWER:
The expression equals 40 (when x = 3)
Answer:
15.25 is your answer
Step-by-step explanation:
Answer:
There is a circle with a diameter[d] of 2.
Step-by-step explanation:
the Radius=diameter /2=2/2=1 units
now
circumference=2πr=2×π×1=6.29=6 units
area=πr²=3.14 unit²
Answer:
-4 or -4/1
Step-by-step explanation:
The equation is in y=mx+b form
m is the slope, and b is the y intercept
So, for this line, y=-4x+10
-4 is the slope and 10 is the y intercept
Hope this helps! :)
