Exercise · ZW-RANDOM-VARIABLE-003 · ★☆☆ Basic
Which of the following is a random variable?
Choose one option.
Show answer
- A. The rule that assigns 1 if a coin lands heads and 0 if it lands tails
Explanation
A random variable is a function from the sample space to the reals. The other options are an event, a number and the sample space itself.
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?
- ZW-RANDOM-VARIABLE-002 Two dice are rolled and X is the sum. How many outcomes of the sample space make up the event \X=4\?
- 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).