∑ZWMath CoursesSyllabusExercises
ES
ZWMath›Probability and statistics›Random variables›Random variable›ZW-RANDOM-VARIABLE-001
Course menu
AreaProbability and statisticsCourseProbability and statisticsTopicRandom variables
Probability foundations6
  • Sample space
  • Event
  • Probability measure
  • Classical probability
  • Addition rule
  • Permutations and combinations
Conditional probability4
  • Conditional probability
  • Independence of events
  • Law of total probability
  • Bayes' theorem
Random variables7
  • Random variable
  • Probability mass function
  • Probability density function
  • Cumulative distribution function
  • Expected value
  • Variance
  • Covariance
Distributions6
  • Bernoulli distribution
  • Binomial distribution
  • Poisson distribution
  • Uniform distribution
  • Exponential distribution
  • Normal distribution
Limit theorems3
  • Chebyshev inequality
  • Law of large numbers
  • Central limit theorem
Statistical inference6
  • Random sample
  • Sample mean
  • Estimator
  • Confidence interval
  • Hypothesis test
  • p-value

Exercise · ZW-RANDOM-VARIABLE-001 · ★☆☆ Basic

Two coins are tossed and \(X\) is the number of heads. What is \(X(\text{HT})\), where H = heads and T = tails?

Choose one option.

Show answer
  • B. 1

← Back to the question

Explanation

The outcome HT has exactly one head, so \(X(\text{HT})=1\).

Study Probability and statistics in ZWMath →

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-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-003 Which of the following is a random variable?
  • 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).

ZW-RANDOM-VARIABLE-002 →

Practice

⏱Exam simulator10 random questions with a grade☰All exercises
◉Open on course✦Open on free study↗Open on the map

ZWMath · Math from definition to practice. Open the interactive map · Syllabus · All exercises

Author: ORCID iD 0009-0009-8641-3511

Privacy · About Speedrunz · Contact