00:01
Here we consider an exponential random variable with a rate parameter equal to 10.
00:07
To answer the probabilities, we are going to make use of the cumulative distribution function for x, that is denoted f of x, and for an exponential random variable, it's equal to 1 minus e to the negative lambda x, for x is greater than or equal to 0.
00:34
For a, we want the probability that the arrival time is less than 0 .3.
00:39
So this is 1 minus e to the negative 10 times 0 .3.
00:59
And this comes out to 0 .9502.
01:07
And for b, we want the probability that x is greater than 0 .3.
01:19
This is equal to 1 minus the probability that x is at most 0 .3.
01:26
And we found the probability that x is less than 0 .9502.
01:34
So this probability is 0 .0498.
01:42
So for c we want the probability that x is between 0 .3 and 0 .5...