I think I started correct but I'm confused towards the end...
A pair of shoes stay in fashion with pdf ke^-.1t for all t>0 where t=1 is 1 year.
T represents the time the shoes go out of fashion.
a) Find k so it's an actual pdf... Just integrate -inf to inf and set = 1... k=.1
b) P(shoes go out of fashion in a month) = P(0<t<1/12)... integrate from 0 to 1/12 = .08%
c) P(shoes go out of fashion between year 1 and 2) = P(1<t<2)... integrate from 1 to 2 = .9%
***Confusing Me (maybe the way it's worded)
d) P(shoes still in style after 10 years) = P(t>10) = 1 - P(t<10) = 1 - integral from 0 to 10 = 94%???
Also, instead of integrating again... is the integral (-.1e^-.1t) my cdf; meaning I could just plug numbers into this? It works but does it make sense to be negative? Shouldn't a cdf measure area to the left of t?
Thanks for any help!
A pair of shoes stay in fashion with pdf ke^-.1t for all t>0 where t=1 is 1 year.
T represents the time the shoes go out of fashion.
a) Find k so it's an actual pdf... Just integrate -inf to inf and set = 1... k=.1
b) P(shoes go out of fashion in a month) = P(0<t<1/12)... integrate from 0 to 1/12 = .08%
c) P(shoes go out of fashion between year 1 and 2) = P(1<t<2)... integrate from 1 to 2 = .9%
***Confusing Me (maybe the way it's worded)
d) P(shoes still in style after 10 years) = P(t>10) = 1 - P(t<10) = 1 - integral from 0 to 10 = 94%???
Also, instead of integrating again... is the integral (-.1e^-.1t) my cdf; meaning I could just plug numbers into this? It works but does it make sense to be negative? Shouldn't a cdf measure area to the left of t?
Thanks for any help!
