A computer writer can make word errors and non-word errors. She makes $i$ word errors in a probability $p_{i,1}$ and $i$ non-word errors in a probability $p_{i,2}$, $\left (\sum_{i=0}^4p_{i,1}=\sum_{i=0}^3p_{i,2}=1\right )$. What is the expected value and standard deviation of number of errors in a text if
a) different type of errors are independent?
b) the Pearson correlation coefficient of the number of different types of errors is $a$?
Is the correct way to compute a) such that I compute $p_i=\sum_{j=0}^ip_{j,1}p_{i-j,2}$ and then compute the expected value of that distribution? And I have no idea how to do b).
