00:01
So, for this problem, to begin, we have that the life of an iphone has an exponential distribution with a mean lifetime of 4 years.
00:12
I'll note that for an exponential, the parameter is 1 over the mean.
00:17
So we have λ is equal to 1 over 4.
00:21
That then means that we have our cumulative distribution function for the probability that x is less than or equal to x is equal to 1 minus e to the power of negative λx.
00:37
So that's going to be 1 minus e to the power of negative x over 4.
00:42
For the first part of the problem, for part a, we're being asked for the probability that x is more than 5.
00:51
Probability that x is greater than 5 is going to be equal to 1 minus the cumulative distribution function evaluated at 5.
00:59
So we'd have 1 minus 1 minus negative e to the power of negative 5 over 4.
01:06
So of course, that's just going to simplify down to e to the power of negative 5 over 4.
01:11
So calculating that out, e to the power of negative 5 over 4, gives us a result of 0 .2865...