STATISTICS 2
Conditions
Conditions: Identifying events that occur randomly, independently, and at a constant average rate. (A)
Conditions: Identifying events that occur randomly, independently, and at a constant average rate. (A)
Conditions: Identifying events that occur randomly, independently, and at a constant average rate. (A)
Calculations
Calculations: Using the Poisson formula for P(X = r) and the cumulative tables. (A)
Calculations: Using the Poisson formula for P(X = r) and the cumulative tables. (A)
Calculations: Using the Poisson formula for P(X = r) and the cumulative tables. (A)
Mean and Variance
Mean and Variance: Understanding that for X ~ Po(λ), E(X) = Var(X) = λ. (A)
Mean and Variance: Understanding that for X ~ Po(λ), E(X) = Var(X) = λ. (B)
Mean and Variance: Understanding that for X ~ Po(λ), E(X) = Var(X) = λ. (C)
Approximating the Binomial
Approximating the Binomial: Using the Poisson distribution as an approximation for B(n, p) when n is large and p is small. (A)
Approximating the Binomial: Using the Poisson distribution as an approximation for B(n, p) when n is large and p is small. (B)
Approximating the Binomial: Using the Poisson distribution as an approximation for B(n, p) when n is large and p is small. (C)
Expectation and Variance
Expectation and Variance: Applying the results E(aX + b) = aE(X) + b and Var(aX + b) = a²Var(X). (A)
Expectation and Variance: Applying the results E(aX + b) = aE(X) + b and Var(aX + b) = a²Var(X). (B)
Expectation and Variance: Applying the results E(aX + b) = aE(X) + b and Var(aX + b) = a²Var(X). (C)
Independent Variables
Independent Variables: Calculating the mean and variance for the sum or difference of
two or more independent variables: E(aX ± bY) = aE(X) ± bE(Y) and Var(aX ± bY) = a²Var(X) + b²Var(Y). (A)
Independent Variables: Calculating the mean and variance for the sum or difference of
two or more independent variables: E(aX ± bY) = aE(X) ± bE(Y) and Var(aX ± bY) = a²Var(X) + b²Var(Y). (B)
Independent Variables: Calculating the mean and variance for the sum or difference of
two or more independent variables: E(aX ± bY) = aE(X) ± bE(Y) and Var(aX ± bY) = a²Var(X) + b²Var(Y). (C)
Normal Combinations
Normal Combinations: Combining independent normal random variables into a single normal distribution. (A)
Normal Combinations: Combining independent normal random variables into a single normal distribution. (B)
Normal Combinations: Combining independent normal random variables into a single normal distribution. (C)
Probability Density Functions (PDF)
Probability Density Functions: Understanding the properties of f(x), including that the total area under the curve equals 1. (A)
Probability Density Functions: Understanding the properties of f(x), including that the total area under the curve equals 1. (B)
Probability Density Functions: Understanding the properties of f(x), including that the total area under the curve equals 1. (C)
Expectation and Variance
Expectation and Variance: Using calculus (integration) to calculate E(X), E(X²), and Var(X) for a given PDF. (A)
Expectation and Variance: Using calculus (integration) to calculate E(X), E(X²), and Var(X) for a given PDF. (B)
Expectation and Variance: Using calculus (integration) to calculate E(X), E(X²), and Var(X) for a given PDF. (C)
Cumulative Distribution Functions (CDF)
Cumulative Distribution Functions: Finding the CDF F(x) by integrating the PDF and using it to find medians and percentiles. (A)
Cumulative Distribution Functions: Finding the CDF F(x) by integrating the PDF and using it to find medians and percentiles. (B)
Cumulative Distribution Functions: Finding the CDF F(x) by integrating the PDF and using it to find medians and percentiles. (C)
Central Limit Theorem
Central Limit Theorem: Understanding that the distribution of the sample mean approaches a normal distribution as the sample size n increases, regardless of the
population distribution. (A)
Central Limit Theorem: Understanding that the distribution of the sample mean approaches a normal distribution as the sample size n increases, regardless of the
population distribution. (B)
Central Limit Theorem: Understanding that the distribution of the sample mean approaches a normal distribution as the sample size n increases, regardless of the
population distribution. (C)
Unbiased Estimators
Unbiased Estimators: Calculating unbiased estimates of the population mean and variance from a sample. (A)
Unbiased Estimators: Calculating unbiased estimates of the population mean and variance from a sample. (B)
Unbiased Estimators: Calculating unbiased estimates of the population mean and variance from a sample. (C)
Confidence Intervals
Confidence Intervals: Constructing and interpreting confidence intervals for the population mean using the normal distribution. (A)
Confidence Intervals: Constructing and interpreting confidence intervals for the population mean using the normal distribution. (B)
Confidence Intervals: Constructing and interpreting confidence intervals for the population mean using the normal distribution. (C)
Formulation
Formulation: Defining the Null Hypothesis (H₀) and Alternative Hypothesis (H₁). (A)
Formulation: Defining the Null Hypothesis (H₀) and Alternative Hypothesis (H₁). (B)
Formulation: Defining the Null Hypothesis (H₀) and Alternative Hypothesis (H₁). (C)
Test Statistics
Test Statistics: Conducting tests for the mean of a normal distribution or parameters of a
Poisson or Binomial distribution. (A)
Test Statistics: Conducting tests for the mean of a normal distribution or parameters of a
Poisson or Binomial distribution. (B)
Test Statistics: Conducting tests for the mean of a normal distribution or parameters of a
Poisson or Binomial distribution. (C)
Significance Levels
Significance Levels: Determining critical regions and p-values to accept or reject the null hypothesis. (A)
Significance Levels: Determining critical regions and p-values to accept or reject the null hypothesis. (B)
Significance Levels: Determining critical regions and p-values to accept or reject the null hypothesis. (C)
Errors: Understanding and identifying Type I and Type II errors in the context of a
statistical test. (A)
Errors: Understanding and identifying Type I and Type II errors in the context of a
statistical test. (B)
Errors: Understanding and identifying Type I and Type II errors in the context of a
statistical test. (C)