00:01
For solving our equation, we use the poisson distribution formula.
00:09
The first point a1, we find the probability that no packets arrive in seconds.
00:16
In 6 seconds, probability no packets arrive in 6 seconds.
00:35
For solving this, first we convert the rate from packets per minute to packets per second.
00:42
So, we change 100 by 16, 100 packets divided by 16.
00:54
So, 5 by 3 packets per second.
01:08
Here, lambda is the packets per second.
01:17
Now, we use the poisson distribution formula for the probability of observing exactly k events in a given time interval is given by probability of k, exactly k events.
01:34
Hence, lambda is the rate of packets per second and t is time equal to e to the power k minus lambda t multiplying lambda t k k divided by k factorial.
02:07
To find the probability of no packets arriving in 6 seconds, we take k equal to 0.
02:15
We substitute k equal to 0 and t equal to 6 into the formula.
02:27
After substituting the values in the formula, we get probability of 0, 5 by 3 multiplied by 6 equal to e to the power k minus 5 by 3 multiplied by 6 multiplied by 5 by 3 divided by 3 multiplied by 6 k 0 divided by 0 factorial...