Many electronics follow a failure rate described by an exponential probability density function (PDF).

Question

 Solar panels are advertised to last 20 years or longer, but panels made in China are failing at a higher rate. The time-to-failure of this device is usually exponentially distributed with mean 5 years. 

What is the probability of failure in the first 10 years? 

Answer 1

x = time to failure

rate = 1/mean = 1/5 = 0.2

P(x < 10) = 1 - e^-0.2*10 = 1 - 0.135 = 0.865