Quiz #2 - Cutoff

• Random variable: a variable that assumed numerical values associated with the random outcomes of an experiment, where 1 numerical value is assigned to each sample point.
• Discrete random variable: random variables that can assume a countable number of values (e.g., whole numbers).
• Continuous random variable: random variables that can assume values corresponding to any of the points within an interval.
• Probability distribution of a discrete random variable: a graph, table, or formula that specified the probability associated with each possible value that a random variable can assume.
• Requirements for the probability distribution of a discrete random variable:

  • Probabilities must be greater than or equal to 0
  • The sum of all probabilities must equal 1
• Binomial random variables must have an experiment consisting of n identical trials.
• Binomial random variables must only have 2 possible outcomes.
• Binomial random variables must have consistent probability for outcomes from trial to trial.
• Binomial random variables must have independent trials.
• Binomial random variables x represent the number of successes in a sample of n trials.
• Poisson distribution: an experiment counting the number of events that occur in a specific variable (e.g., time, area, volume, etc.).
• e = 2.71828
• For a Poisson random variable, λ represents the mean.
• This formula represents the probability distribution for a Poisson random variable.

  
• This formula represents the mean for a Poisson random variable.

  
• This formula represents the variance for a Poisson random variable.

  
• The probability distribution for a continuous random variable can be represented by a smooth curve where the probability that x falls between 2 values is the area under the curve between those values.
• Uniform probability distribution: continuous random variables that appear to have equally likely outcomes over their range of possible values.
• Normal probability distribution: a perfectly symmetric, bell shaped distribution about its mean and whose spread is determined by standard deviations.
• Standard normal distribution: a normal distribution with a mean of 0 and standard deviation of 1.
• Standard normal random variable: a random variable with a standard normal distribution.
• Parameter: a numerical descriptive measure of a population.
• Sample statistic: a numerical descriptive measure of a sample.
• Sample distribution: the probability distribution of a sample statistic.