propability

Alicia · #1 $Old$ April 15th, 2008, 10:06 PM

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.

flyingsquirrel · #2 $Old$ April 16th, 2008, 12:12 AM

Hello

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

(b) The expected value of the profit is given by $\int_{-\infty}^{\infty}xf(x)\,\mathrm{d}x$ .