Roll 2 fair dice, find pdf and cdf

[srk827]

Hi guys. I have a test tomorrow and I am trying to work out the problems on the review sheet, but I can't figure out this one dealing with pdf and cdf.

Roll 2 fair dice and call each outcome (i,j) where i,j = 1,2,...6.
Define: X= {i+j if i+j ≤ 6 ; abs.value(i-j) otherwise}

A) Find and draw the pdf.
B) Find and draw the cdf.



The professor sent us the solutions. I just can't figure out how he got it. The solution he sent was:

a)
f(x)= { 3/36 if x=o; 5/36 if x=2 or 4 or 6; 6/36 if x=1 or 3 or 5}

b) f(x)= {0 if x<0; 3/36 if 0≤x<1; 9/36 if 1≤x<2; 14/36 if 2≤x<3; 20/36 if 3≤x<4; 25/36 if 4≤x<5; 31/36 if 5≤x<6; 1 if x≥6}

Could someone please help me understand the steps to take to get this answer?

 

[Ray Vickson]

Hi guys. I have a test tomorrow and I am trying to work out the problems on the review sheet, but I can't figure out this one dealing with pdf and cdf.

Roll 2 fair dice and call each outcome (i,j) where i,j = 1,2,...6.
Define: X= {i+j if i+j ≤ 6 ; abs.value(i-j) otherwise}

A) Find and draw the pdf.
B) Find and draw the cdf.



The professor sent us the solutions. I just can't figure out how he got it. The solution he sent was:

a)
f(x)= { 3/36 if x=o; 5/36 if x=2 or 4 or 6; 6/36 if x=1 or 3 or 5}

b) f(x)= {0 if x<0; 3/36 if 0≤x<1; 9/36 if 1≤x<2; 14/36 if 2≤x<3; 20/36 if 3≤x<4; 25/36 if 4≤x<5; 31/36 if 5≤x<6; 1 if x≥6}

Could someone please help me understand the steps to take to get this answer?

First find the probabilities of all the individual pairs (i,j). For each pair (i,j), figure out what x must be. Of course, the same x might be obtained for several different pairs (i,j), so you need to be careful. That's it; that's all there is to it.

RGV