Exercise · ZW-RANDOM-VARIABLE-010 · ★★★ Advanced
With two dice, let \(S=a+b\) and \(T=2a\) (where \(a\) is the first die). Compute \(P(T=2)+P(S=2)\).
Choose one option.
Show answer
- B. 7/36
Explanation
\(P(T=2)=P(a=1)=\tfrac16\), while \(S=2\) requires \(a=b=1\): \(\tfrac1{36}\). They add up to \(\tfrac7{36}\). \(S\) and \(T\) are different variables even though both depend on \(a\).
Review the concept: Random variable
A random variable \(X\) is a function that assigns a real number to each outcome of the sample space \(\Omega\) of a random experiment.
\[X:\Omega\to\mathbb{R}\]
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