Asked by Ali
The question asked whether or not f(x) = 0.5e^x when x is less than or equal to zero and f(x) = 0.5e^(-x) when x is greater than or equal to zero is a valid probability density.
I know that it is the integral... but usually you have a domain that is not a single point. Should I increase the domain slightly??
I know that it is the integral... but usually you have a domain that is not a single point. Should I increase the domain slightly??
Answers
Answered by
Steve
huh? Looks to me like the domain is all real numbers. The fact that x=0 is included in both parts doesn't really matter, since e^0 = e^-0 = 1
So, since the functions are symmetric, all you need is
∫[0,∞] 0.5 e^-x dx = 1/2
So, since the functions are symmetric, all you need is
∫[0,∞] 0.5 e^-x dx = 1/2
Answered by
Ali
OH MY GOODNEss! I never even thought of that! Thank you so much!
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