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Further Statistics 1: lesson checks flashcards

This deck has 9 check-yourself questions and 8 spot-the-error cards. The misconception each lesson corrects, and its check-yourself question with the worked answer. Rate each answer, and the card comes back sooner or later depending on how you rated it.

Further Maths · all 584 maths cards

How the five kinds differ

Standard results ask you to recall a formula or a value. Definitions ask you to state a mathematical term precisely. Recall prompts ask for a rule, condition or method. Check yourself cards are a short question with its answer. Spot the error cards ask you to correct a statement that is wrong.

Every card in this deck

Choose any card to try it in the player above. Each card links to the lesson that teaches it.

• The expected value is the outcome you should expect to see most often.Spot the error
• X has E(X) = 4 and Var(X) = 9. Find E(3X − 2) and Var(3X − 2).Check
• The Poisson distribution needs both a number of trials and a probability, just as the binomial does.Spot the error
• Accidents at a junction follow Po(2) per week. Find the mean and variance of the number of accidents in a four-week month.Check
• Waiting for a success is just the binomial distribution read backwards, so the same formulae apply.Spot the error
• A biased coin shows heads with probability 0.25. Find the probability that the first head appears on the fourth toss, and the mean number of tosses required.Check
• Because the Poisson distribution has no fixed number of trials, hypothesis testing cannot be applied to it.Spot the error
• For a Poisson model with H₀: λ = 4 and H₁: λ > 4, the observed value is 9 and P(X ≥ 9) = 0.0214. State the conclusion at the 5% level.Check
• The sample mean can only be treated as normal when the population it comes from is itself normal.Spot the error
• A distribution has mean 30 and variance 100. Write down the approximate distribution of the mean of a sample of 25, and of the total of the 25.Check
• A large chi-squared statistic proves the model is wrong; a small one proves it is right.Spot the error
• A goodness-of-fit test uses 5 classes after pooling, with the distribution's single parameter estimated from the data. State the degrees of freedom.Check
• Expected frequencies in a contingency table come from assuming every cell is equally likely.Spot the error
• A contingency table has 3 rows and 4 columns. State the degrees of freedom, and find the expected frequency for a cell whose row total is 40 and column total is 30, with grand total 200.Check
• A generating function is just a compact way to write a distribution; it cannot tell you anything new.Spot the error
• A random variable has G(t) = (0.4 + 0.6t)⁵. Name the distribution and write down its mean.Check
• A test has size 0.043 and, at a particular alternative, a probability of 0.68 of failing to reject H₀. State the probability of a Type I error and the power at that alternative.Check

The lessons these cards come from

• Contingency tables
• Discrete random variables and expectation
• Geometric and negative binomial distributions
• Goodness-of-fit tests
• Hypothesis tests for Poisson and geometric models
• Probability generating functions
• The Central Limit Theorem
• The Poisson distribution
• Type I and Type II errors, test size and power

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