Exercise · ZW-RANDOM-VARIABLE-005 · ★★☆ Intermediate
Two dice are rolled and \(X\) is the larger of the two results. Compute \(P(X=6)\).
Choose one option.
Show answer
- C. 11/36
Explanation
\(\{X=6\}\) contains the pairs where at least one die shows 6: \(6+6-1=11\) out of 36. Counting only 6 outcomes ignores that the 6 can be on the other die.
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.
\[X:\Omega\to\mathbb{R}\]
More practice problems: random variable
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- ZW-RANDOM-VARIABLE-003 Which of the following is a random variable?
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- ZW-RANDOM-VARIABLE-006 Two dice are rolled and Y=|a-b| is the absolute difference of the results. Compute P(Y=0).
- ZW-RANDOM-VARIABLE-007 Which of the following random variables is continuous?
- ZW-RANDOM-VARIABLE-008 Two fair coins are tossed and X is the number of heads. Compute P(X≥ 1).
- ZW-RANDOM-VARIABLE-009 Let Omega=\-2,-1,0,1,2\ with equally likely outcomes and X(ω)=ω^2. Compute P(X=1).