Suppose you have a lightbulb which has an average time to fail of 5 days. The failure can be modelled as a geometric distribution. What is the probability of 2 bulbs failing within seven days?
Currently I have used the formula E[x]=1/p so p=1/5 = 0.2.
From there, I thought, well, a device might fail on day one and the second within the next six days, and a second possibility is that the device fails within the first two days and the second within the next 5 days, so:
[(cumulative density of failing at day 1) X (cumulative density of 6 days)] + [(cumulative density of failing at day 2) X (cumulative density of 5 days)]...
and so on...
but I get a value over 1 which I don't think would be correct?
Any advice on how to approach multiplying cumulative densities