Exercise · ZW-RANDOM-VARIABLE-002 · ★☆☆ Basic
Two dice are rolled and \(X\) is the sum. How many outcomes of the sample space make up the event \(\{X=4\}\)?
Choose one option.
Show answer
- C. 3
Explanation
They are \((1,3)\), \((2,2)\) and \((3,1)\). It is easy to forget that \((1,3)\) and \((3,1)\) are different outcomes.
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
- ZW-RANDOM-VARIABLE-001 Two coins are tossed and X is the number of heads. What is X(HT), where H = heads and T = tails?
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- ZW-RANDOM-VARIABLE-004 Three coins are tossed and X is the number of heads. What is the set of possible values of X?
- ZW-RANDOM-VARIABLE-005 Two dice are rolled and X is the larger of the two results. Compute P(X=6).
- 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).