SOLUTION: Please help me solve this problem : Find k so that the function given by p(x) = k /(x + 1), x = 1, 2, 3, 4 is a probability function. Graph the density and cumulative di

Algebra ->  Probability-and-statistics -> SOLUTION: Please help me solve this problem : Find k so that the function given by p(x) = k /(x + 1), x = 1, 2, 3, 4 is a probability function. Graph the density and cumulative di      Log On


   

Question 1177286: Please help me solve this problem :
Find k so that the function given by
p(x) = k /(x + 1), x = 1, 2, 3, 4
is a probability function. Graph the density and cumulative distribution functions.
Thank you
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
p%28x%29+=+k%2F%28x+%2B+1%29, x = 1, 2, 3, 4

the sum of the values must be 1.



k%2F2%2Bk%2F3%2Bk%2F4%2Bk%2F5=1

Multiply by LCM = 60

60k%2F2%2B60k%2F3%2B60k%2F4%2B60k%2F5=60

30k%2B20k%2B15k%2B12k=60

77k=60

k=60%2F77

p%28x%29+=+k%2F%28x+%2B+1%29

p%28x%29+=+%2860%2F77%29%2F%28x+%2B+1%5E%22%22%29

Multiply top and bottom by 77

p%28x%29+=+60%2F%2877%28x+%2B+1%29%29

p%281%29+=+60%2F%2877%281+%2B+1%29%29=60%2F%28%2877%29%282%29%29=30%2F77

p%282%29+=+60%2F%2877%282+%2B+1%29%29=60%2F%28%2877%29%283%29%29=20%2F77

p%283%29+=+60%2F%2877%283+%2B+1%29%29=60%2F%28%2877%29%284%29%29=15%2F77

p%284%29+=+60%2F%2877%284+%2B+1%29%29=60%2F%28%2877%29%285%29%29=12%2F77


Graph of probability function 

p%28x%29+=+60%2F%2877%28x+%2B+1%29%29 x = 1, 2, 3, 4



To get the the cumulative distribution function: 

c%281%29+=+p%281%29+=+30%2F77

c%282%29+=+P%281%29%2Bp%282%29+=30%2F77%2B20%2F77=50%2F77

c%283%29+=+P%281%29%2Bp%282%29%2Bp%283%29+=30%2F77%2B20%2F77%2B15%2F77=65%2F77 



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



Edwin