Increment of probability with number of motifs random fragments

More calculations….

This post is part of my thought process to try to understand the preliminary analysis that I have to do (read last two posts).

In the previous post I calculated the distribution of random fragments from a given size of fragment according to binomial distribution.

Than I calculated the increase expected in the distribution, if have 1 or more motifs increase the probability at a certain rate.  What I did was

First decreasing frequency when I have 0 motifs (x = 0)

The decreased amount divided by the total number of motifs present was added to each frequency with one or more fragments

This calculation however is wrong since I am not taking in account that the increase in frequency has to be proportional

For instance:

if my input is:

X =     0         1       2        3       4

# =    100   200   300   200   100

and 10% are taken up 90/900:

# =    10     20     30      20      10

Fx =   0.111  0.222  0.333 0.222 0.111

now what if having X >= 1 increase 2 fold

# =    10           40       60       40      20

Fx =   0.058  0.235  0.353 0.235 0.118

This same strategy can be used when the probability increases with the number of motifs as if each motif increment probability 5%:

prb  10%    15%     20%    25%    30%

#      10       30        60        50       30

Fx = 0.055  0.166  0.33   0.27     0.166

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