
Using this formula I got 0
Where :
Random number (K) = 3
Time interval (t)= 10
Parameter Rate(a) = 10
e = 2.71828
The formula is correct, I have seen my error :
Random number (K) = 3
Time interval (t)= 10
Parameter Rate(a) = 1/10 =0.1
e = 2.71828
Probability of 3 blocks mined in an average of 10 minutes = 0.06132
My interpretation is if the exactly is :
With in the 10 minutes time interval
0 to infinite block can be mined while though my constrict is 3 block
Then
Pr (3 block) = 1 - (Pr( ≤2 block) + Pr (>3 block)
Where :
Pr( ≤2 block) = Pr (0 block) + Pr (1 block) + Pr (2 block)
Pr (>3 block) = Pr (4 block) + Pr (5 block) + Pr (6 block)...
Though this tends to infinity but I stop in block 6 since I'm using 5 decimal place
But my final answer was Pr(3 block) = 0.06133 which is the similar to the Probability of 3 blocks mined in an average of 10 minutes = 0.06132