Consider rolling two fair six sided dice with faces numbered 1, 2, 3, 4, 5, 6. (a) write out the sample space for one roll of the two dice. (b) let x be the result of the first die and y be the result of the second die. consider the random variable z = |x − y |, the absolute value of the difference of the first die minus the second die. what is the sample space for z? (c) what is the expected value of z? (d) write out the cumulative distribution function in tabular form for the random variable z

a. The sample space for has 36 possible outcomes,

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),

(2, 1), (2, 2), (2, 3), ...,

(3, 1), (3, 2), ...,

and so on.

b. In the array above, replace each coordinate pair with the absolute difference between the coordinates; you'd end up with an array like

0, 1, 2, 3, 4, 5,

1, 0, 1, 2, 3, 4,

2, 1, 0, 1, 2, 3,

3, 2, 1, 0, 1, 2,

4, 3, 2, 1, 0, 1,

5, 4, 3, 2, 1, 0

so that the sample space for is the set of integers, {0, 1, 2, 3, 4, 5}.

c. The sample space above illustrates that

so the expected value of is

d. Not sure what you mean by "tabular form", but you can obtain the CDF from the usual definition,

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

dude thats to long figure it

step-by-step explanation: