Closed vashcast closed 2 years ago
In the current status of the solution it is used that $\mathbb{P}(Z_i>x/n)=\int_0^{x/n} f(u) \rm{d}u$, $F(0)=1$, and $F'(0)= -\lambda$. None of these statements are correct.
The correct statements are:
$\mathbb{P}(Z_i>x/n)=\int_0^{\infty} f(u) \rm{d}u - \int_0^{x/n} f(u) \rm{d}u= 1 - \int_0^{x/n} f(u) \rm{d}u$ = 1 - F(x/n).
$F(0) = \int_0^0 f(u) \rm{d}u = 0$.
$F'(0) = \lim_{x \to 0} f(x) = \lambda$.
All these changes lead us to the same expected result.
fixed, thank you
telmo-correa
commented
2 years ago
In the current status of the solution it is used that $\mathbb{P}(Z_i>x/n)=\int_0^{x/n} f(u) \rm{d}u$, $F(0)=1$, and $F'(0)= -\lambda$. None of these statements are correct.
The correct statements are:
$\mathbb{P}(Z_i>x/n)=\int_0^{\infty} f(u) \rm{d}u - \int_0^{x/n} f(u) \rm{d}u= 1 - \int_0^{x/n} f(u) \rm{d}u$ = 1 - F(x/n).
$F(0) = \int_0^0 f(u) \rm{d}u = 0$.
$F'(0) = \lim_{x \to 0} f(x) = \lambda$.
All these changes lead us to the same expected result.