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propability
Hi guys,
Im new to the forum and this is my first post. I am in very urgent need of some help I have been practising some prob & stat for an exam, tomorrow and have been doing pretty well till I came upon this question. Can anyone help I dont understand this topic very well and I have reason to believe that a similar question will come on the exam tomorrow I want to know how to go about doing it thanks in advance.
Alicia
The question is attached. Thanks a million.

Hello
(a) The probability that the profit is lower than $\displaystyle u$ is $\displaystyle P(X\leq u)=\int_{\infty}^uf(x)\,\mathrm{d}x$. If you want to know the probability that the profit is between $\displaystyle u$ and $\displaystyle v$ ($\displaystyle u<v$), you'll have to evaluate the probability that it is lower than $\displaystyle v$ and greater than $\displaystyle u$ : it boils down to calculating $\displaystyle P(X\leq v)P(X\leq u) = \int_{\infty}^vf(x)\,\mathrm{d}x
\int_{\infty}^uf(x)\,\mathrm{d}x = \int_u^vf(x)\,\mathrm{d}x$ because if the profit is lower than $\displaystyle v$ it is necessarily lower than $\displaystyle u$.
(b) The expected value of the profit is given by $\displaystyle \int_{\infty}^{\infty}xf(x)\,\mathrm{d}x$.