Question 1177286
<pre>
{{{p(x) = k/(x + 1)}}}, x = 1, 2, 3, 4

the sum of the values must be 1.

{{{k/(1+1)+k/(2+1)+k/(3+1)+k/(4+1)=k/2+k/3+k/4+k/5=1}}}

{{{k/2+k/3+k/4+k/5=1}}}

Multiply by LCM = 60

{{{60k/2+60k/3+60k/4+60k/5=60}}}

{{{30k+20k+15k+12k=60}}}

{{{77k=60}}}

{{{k=60/77}}}

{{{p(x) = k/(x + 1)}}}

{{{p(x) = (60/77)/(x + 1^"")}}}

Multiply top and bottom by 77

{{{p(x) = 60/(77(x + 1))}}}

{{{p(1) = 60/(77(1 + 1))=60/((77)(2))=30/77}}}

{{{p(2) = 60/(77(2 + 1))=60/((77)(3))=20/77}}}

{{{p(3) = 60/(77(3 + 1))=60/((77)(4))=15/77}}}

{{{p(4) = 60/(77(4 + 1))=60/((77)(5))=12/77}}}


Graph of probability function 

{{{p(x) = 60/(77(x + 1))}}} x = 1, 2, 3, 4

{{{drawing(400,200,-1,4,-1,4,

line(0,0,3,0), line(0,0,0,3), line(1,0,1,2),  line(2,0,2,1.5),  line(3,0,3,1.2),

locate(-.05,0,1),locate(-.05+1,0,2),locate(-.05+2,0,3),locate(-.05+3,0,4),

locate(-.1,3.9,30/77),locate(1-.1,2.9,20/77),locate(2-.1,2.4,15/77),locate(3-.1,2.2,12/77) 

 )}}}

To get the the cumulative distribution function: 

{{{c(1) = p(1) = 30/77}}}

{{{c(2) = P(1)+p(2) =30/77+20/77=50/77}}}

{{{c(3) = P(1)+p(2)+p(3) =30/77+20/77+15/77=65/77}}} 

{{{c(4) = P(1)+p(2)+p(3)+p(4) =30/77+20/77+15/77+12/77=77/77=1}}}

Here's the graph of the cumulative distribution function which accumulates
as it goes:

{{{drawing(400,550,-1,4,-1,11,

line(0,0,3,0), line(0,0,0,3), line(1,0,1,5),  line(2,0,2,6.5),  line(3,0,3,10),

locate(-.05,0,1),locate(-.05+1,0,2),locate(-.05+2,0,3),locate(-.05+3,0,4),

locate(-.1,3.9,30/77),locate(1-.1,5.9,50/77),locate(2-.1,7.4,65/77),locate(3-.1,11,77/77=1) 

 )}}}

Edwin</pre>