Exercise · ZW-PROBABILITY-MASS-FUNCTION-009 · ★★★ Advanced
Let \(p(x)=\left(\tfrac12\right)^x\) for \(x=1,2,3,\dots\). Compute the probability that \(X\) is even.
Choose one option.
Show answer
- D. 1/3
Explanation
Add \(\tfrac14+\tfrac1{16}+\cdots\), a geometric series with ratio \(\tfrac14\): \(\dfrac{1/4}{1-1/4}=\tfrac13\). The odd values contribute the remaining \(\tfrac23\).
Review the concept: Probability mass function
The probability mass function \(p_X\) of a discrete random variable \(X\) gives, for each value \(x\) it can take, the probability \(P\) that it takes it.
\[p_X(x)=P(X=x)\]
More practice problems: probability mass function
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