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CDF of a function of 2 random variables
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[QUOTE="vortmax, post: 3603905, member: 43898"] [h2]Homework Statement [/h2] Two toys are started at the same time each with a different battery. The first battery has a lifetime that is exponentially distributed with mean 100 min; the second battery has a lifetime that is Rayleigh-distributed with a mean 100 minutes. a) Find the CDF to the time T until the battery in a toy first runs out b) Suppose that both toys are still operational at 100 minutes. Find the CDF of the time T2 that subsequently elapses until the battery in a toy first runs out c) in part b, find the cdf to the total time that elapses until a battery first fails. [h2]Homework Equations[/h2] [u]Exponential Dist[/u] [itex]f(T) = \lambda e^{-\lambda T}[/itex] [itex] F(T) = 1 - e^{-\lambda T}[/itex] [u]Rayleigh-dist[/u] [itex]f(T) = \frac{T}{\alpha^2} e^{\frac{-T}{2\alpha^2}}[/itex] [itex]F(T) = 1 - e^{\frac{-T}{2\alpha^2}}[/itex] [h2]The Attempt at a Solution[/h2] First, I calculated values for lambda and alpha based on the means ... but this part isn't entirely necessary to the final solution. a) I need to find the cdf of the function: [itex] T = min(T_1,T_2)[/itex] where [itex]T_1[/itex] and [itex]T_2[/itex] are the two RV's respectively... but I'm really at a loss about how to proceed. [/QUOTE]
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CDF of a function of 2 random variables
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