QE 1/2 - intro to probability and stats Flashcards
What does the skewness of a distribution represent?
Asymmetry
Example of positively skewed distribution
Income
Example of negatively skewed distribution
Age
Requirements for use of Binomial distribution?
- Fixed no. trials
- 2 possible outcomes (success/fail)
- Independent outcomes
- Constant probability of success
2 variables independent iff…
- Joint probability = product of marginal probabilities
2. Probability of X given Y = probability of X
Desirable characteristics of an estimator?
- Unbiasedness
- Consistency
- Efficiency
Properties of the sample mean
BEST LINEAR UNBIASED ESTIMATOR (BLUE)
- Unbiased
- Consistent
- Most efficient of all unbiased estimators that are weighted averages of y1, y2,…,yn
What does ‘almost sure’ convergence mean?
Always converges, except on things that never converge
Why does mean square convergence imply probability convergence?
Markov’s inequality
Steps of a hypothesis test
- State null hypothesis and alternative hypothesis
- Calculate test statistic
- Derive its asymptotic distribution using CLT (and state test statistic’s distribution under the null hypothesis)
- Compare to appropriate critical value (depending on significance level)
- State whether you reject/fail to reject null the null hypothesis
How to help remember F-stat formula?
- F-stats must positive
2. Want to make the denominator as small as possible
What does it mean for a test to have high/low power?
- High power - when alternative hypothesis true, test likely to reject null hypothesis
- Low power - when alternative hypothesis true, test unlikely to reject null hypothesis
What is the difference between the sample mean and the population mean?
Sample mean - a function of the data (random variable); estimator of the population mean
Population mean - a parameter
