Basic Statistics20815 marksNumerical: expected value and varianceExpected value and decision making
A tech support team handles the following number of customer queries (X) per hour along with their probabilities. Find the expected number and variance of queries handled per hour.
A tech support team handles the following number of customer queries (X) per hour along with their probabilities. Find the expected number and variance of queries handled per hour.
$$\begin{array}{|c|ccccc|}\hline X & 0 & 1 & 2 & 3 & 4 \ \hline P(X) & 0.10 & 0.20 & 0.30 & 0.25 & 0.15 \ \hline \end{array}$$
[5]
X 0 1 2 3 4 ------------------ P(X) 0.10 0.20 0.30 0.25 0.15 Check: $\sum P(X) = 0.10 + 0.20 + 0.30 + 0.25 + 0.15 = 1.00$ ✓ (valid distribution) --- $$E(X) = \sum X \cdot P(X)$$ X P(X) X·P(X) ----------------- 0 0.10 0.00 1 0.20 0.20 2 0.30 0.60 3 0.25 0.75 4 0.15 0.60 $$E(X) = 0 + 0.20 + 0.60 + ...