1. ## 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.

2. 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 $\displaystyle \int_{-\infty}^{\infty}xf(x)\,\mathrm{d}x$.