Question: Problem #6: An electrical current traveling through a resistor may take one of three different paths, with probabilities \({{p}_{1}}=0.25\), \({{p}_{2}}=0.30\), and \({{p}_{3}}=0.45\), respectively. Suppose we monitor the path taken in \(n=10\) consecutive trials.

(a) Find the probability that the electrical current will travel the first path \({{y}_{1}}=2\) times, the second path \({{y}_{2}}=4\) times, and the third path \({{y}_{3}}=4\) times.

(b) Find \(E({{y}_{2}})\) and \(\operatorname{var}({{y}_{2}})\). Interpret the results.