00:01
We are given the probability density function shown here, and we are asked to calculate some probabilities.
00:07
So since we are calculating probabilities, let's first define the cdf for the distribution.
00:14
And let's define the cdf for x is at least 0 .5, because that is the domain for which the questions on probability pertain.
00:25
So this is given by 0 .5 to x.
00:48
And this can be re -expressed like this.
01:33
And this is evaluated over 0 .5 to and this gives us 1 minus e to the 0 .075 times e to the negative 0 .15 x.
02:32
And remember this is for x greater than or equal to 0 .5.
02:40
Now for part a we want the probability that x is at most six seconds.
02:50
So this is f at six.
02:54
It's the cdf evaluated at six, and this comes out to about 0 .562...