Hi, i've tried to solve this problem, but i have only ideas. Can you tell me if this is the way to solve this problem?. Thanks in advance!

Problem:

Resistance $\displaystyle R_1$ has a mean value of 330 ohms with a tolerance of 1% corresponding to 3 standard deviations. $\displaystyle R_1$ has an gaussian distribution. If

$\displaystyle V_2 = \frac{R_2}{R_1+R_2}V$ and

$\displaystyle V_1=\frac{R_1}{R_1+R_2}V$

where, V is a 9 Volts constant voltage and $\displaystyle R_2$ has a value of 330 ohms.

  1. Calulate the mean and variance of $\displaystyle V_2$
  2. Calculate the pdf of $\displaystyle V_2$


My ideas:

Only $\displaystyle V_2$ and $\displaystyle R_1$ are random variables, and $\displaystyle V_2$ is a function of $\displaystyle R_1$, thus $\displaystyle V_2 = g(R_1)$. So, for the mean of $\displaystyle V_2$:

$\displaystyle E[V_2]=\int{g(r_1)f_{R_1}(r_1)dr_1}$

right??

Or, should i calculate first the cdf with

$\displaystyle F_{V_2}(v_2)=\int{f_{R_1}(r_1)}dr_1$

or, directly the pdf with

$\displaystyle f_{V_2}(v_2)=f_{R_1}(r_1)\Big|\frac{dx}{dy}\Big|$

Can you give me some tips and hints??

Thank you all!!