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

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

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

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

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


My ideas:

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

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

right??

Or, should i calculate first the cdf with

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

or, directly the pdf with

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!!