- #1
Askhwhelp
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$$f(y) = \begin{cases} \int_0^y\frac1\beta e^{\frac {-t}\beta}dt = -e^{\frac {-y}\beta}+1 & \text{for } 0 ≤ y < ∞,\\ 0& \text{for } elsewhere\end{cases}$$
P(Y>3) = 1 - P(Y ≤ 3) = 1 - (-e^{-3/beta}+1) = .1353
When I take log to both sides, I get 3.453.
When I take ln to both sides, I get 1.4998. When I plug it back into the equation, 1.4998 looks right...However, I puzzle why there is a difference?
Before this, could anyone please make sure beta = 1.4998?
(1) P(Y<0) = 0, right?
(2) P(Y<1) = -e^{1/1.4998} + 1 = .4866 , right?
P(Y>3) = 1 - P(Y ≤ 3) = 1 - (-e^{-3/beta}+1) = .1353
When I take log to both sides, I get 3.453.
When I take ln to both sides, I get 1.4998. When I plug it back into the equation, 1.4998 looks right...However, I puzzle why there is a difference?
Before this, could anyone please make sure beta = 1.4998?
(1) P(Y<0) = 0, right?
(2) P(Y<1) = -e^{1/1.4998} + 1 = .4866 , right?
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