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)
Answer: C
Step-by-step explanation:
I recognize this as coming from an old 1912 novel published as "A Princess of Mars", by Edgar Rice Burroughs. I read the book as a teenage boy. A 2012 movie, called "John Carter", was based on this same book.
Answer A - No, because the character (Carter) says, "My muscles, perfectly attuned and accustomed to the force of gravity on Earth". Perfectly attuned is an athlete, not a clumsy person.
Answer B - No, because the character just doesn't sound all that frustrated. The experience is strange and inconvenient, yet he is handling his emotions pretty well for how weird it must be. It is more like he is writing about an amazing experience, not just complaining.
Answer D - No, because he never says that the experience was making him happy. He does not say that he was laughing or smiling or that it reminded him of some pleasant time he had as a boy.
Answer C - Yes. - Creation of vivid imagery. In a novel, the author must paint pictures with their words. Part of how the author does this is by giving you the picture of a man who feels very comfortable with his coordination on Earth, but keeps winding up about 9 feet off the ground without trying. He doesn't just "I kept falling". He tells you in vivid detail - "... landed me sprawling on my face or back ..."
Hope this helps!
Answer:
(-3, 5), (1, 4), (-2, 3), and (0, 2).
Step-by-step explanation:
When a function is inverted, the x-values become y-values, and the y-values become x-values.
The ordered pairs for the function are (5, -3), (4, 1), (3, -2), and (2, 0).
After inversion, the ordered pairs will be (-3, 5), (1, 4), (-2, 3), and (0, 2).
Hope this helps!
