calculating an exponential distribution problem

37 Views Asked by At

I am given this fairly-easy question, yet I cannot find a reasonable solution.

The time it takes to stare at an object is approx. 20ms. The waiting time distribution is exponential:

$$f(x)= \lambda e^{-\lambda x} ; F(x)=1-e^{-\lambda x}$$

1) Calculate the probability that you are able to stare at an object in the first 100ms after opening your eyes.
2) Calculate the probability of staring a three different objects in the first 900ms after opening your eyes.

I have tried to answer the first question in this way:
$$F(x)=F(100ms=\frac{1}{10}s)=1-e^{-(\frac{1}{10}*\frac{2}{100})*1}$$ where $(\frac{1}{10}*\frac{2}{100})$ is $\lambda$ and x is 1, as "starting one object".

Similarly, the second answer would be: $$F(x)=F(900ms=\frac{9}{10}s)=1-e^{-(\frac{9}{10}*\frac{2}{100})*3}$$ but I'm far from saying that I'm sure of what I've done.

I am aware that this might be a huge duplicate question, but I haven't been able to find a similar question, I'm sorry if I've done something wrong.