# Computing the expected value and standard deviation of two distributions

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).

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Hint: $E[X+Y] = E[X]+E[Y]$. $\text{var}(X+Y) = \text{var}(X)+\text{var}(Y)+2\rho\sqrt{\text{var}(X)\text{var}(Y)}$. –  Dilip Sarwate Nov 9 '12 at 15:11
OK. I got it. Thanks! –  student Nov 9 '12 at 15:47