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[Step-by-Step] 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,

Question: 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.

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

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[Step-by-Step] 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,

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