Question :
The length of time(in hundreds
The length of time(in hundreds of hours) for the failure of a transistor is a random variable Y with distribution function ;
F(Y) = { 0 : if y<0 or [1 - e^(-(y^2) ] if y>=0 }
Find the probability that the transistor operates for at least 200 hours.
Since we need to find the probability that the transistor operates for at least 200 hours, we nedd to find, P(Y>=200) = integrate [f(t) dt] from -infinity to 200.
P(Y>=200) = integrate [ 0 dt] from -infinity to 0 + integrate [1 - (e^(-(t^2))) dt] from 0 to 200
==> P(Y>=200) = 0 + integrate [1 - (e^(-(t^2))) dt] from 0 to 200
==> P(Y>=200) = integrate [1 - (e^(-(t^2))) dt] from 0 to 200
==> P(Y>=200) = integrate [1 dt ] from 0 to 200 + integrate [ - (e^(-(t^2))) dt] from 0 to 200
But, how do we the following integration? I'm having trouble finding a suitable substitution or any other method for the following integration ; I = integrate [1 - (e^(-(t^2))) dt] from 0 to 200
Or is there any other method we can use to do this problem?
Thank you!
0 answers