AQA A level further maths paper 3 - statistics question

Hi everyone I'd be so grateful if someone can answer this.
So I'm sitting paper 3 tomorrow and there's one thing I'm a little fuzzy on and I just can't find any answers by googling.

With the exponential distribution, there's a way to find F(x) first without using f(x). In my textbook it says "P(T<t)=1-P(T>t)=1-P(no occurrences in interval t)=1-e^(-xt)" (x is the parameter and 1/x is the mean). I understand it all except I have no idea how to get p(no occurrences in interval t). I was thinking perhaps it's the formula for Poisson with x=0? But then I don't know why there is now a t there. I've seen a few questions asking to find F(x) so I want to understand this in case it comes up tomorrow. Thank you!

Reply 1

old_engineer

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Original post by entitree

Hi everyone I'd be so grateful if someone can answer this.
So I'm sitting paper 3 tomorrow and there's one thing I'm a little fuzzy on and I just can't find any answers by googling.

With the exponential distribution, there's a way to find F(x) first without using f(x). In my textbook it says "P(T<t)=1-P(T>t)=1-P(no occurrences in interval t)=1-e^(-xt)" (x is the parameter and 1/x is the mean). I understand it all except I have no idea how to get p(no occurrences in interval t). I was thinking perhaps it's the formula for Poisson with x=0? But then I don't know why there is now a t there. I've seen a few questions asking to find F(x) so I want to understand this in case it comes up tomorrow. Thank you!