Chapter 5: Further Statistics 1: Probability Generating Functions

A-level Further MathsFurther Statistics 1 & 23 topicsHigher

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Further Statistics 1: Probability Generating Functions: Edexcel Further Maths Optional Long-Answer Questions

Examiner-style long-answer practice with automatic marking, improvement advice and ProofCoach tracking.

4 questions32 marks64 min

standard / hard / synoptic

8 marksfindstandardEdexcel

FS05-1 Find the required result for Further Statistics 1: Probability Generating Functions. Given A random variable X has PGF

G(t) = (0

.3 + 0.

7t)^{5}

. Use differentiate the PGF to find mean and variance and identify the distribution. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

Write your answer first, then mark it.

8 marksshow thathardEdexcel

FS05-2 Show that X has binomial distribution B(5, 0.7) for Further Statistics 1: Probability Generating Functions. Start from A random variable X has PGF

G(t) = (0

.3 + 0.

7t)^{5}

. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

Write your answer first, then mark it.

8 marksdeterminehardEdexcel

FS05-3 Determine the requested value in this structured Further Statistics 1: Probability Generating Functions problem: find the PGF of X + Y where Y has PGF 0.4 + 0.6t. Use the same data: A random variable X has PGF

G(t) = (0

.3 + 0.

7t)^{5}

. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

Write your answer first, then mark it.

8 markshencesynopticEdexcel

FS05-4 Hence use the result X has binomial distribution B(5, 0.7) to complete the extension for Further Statistics 1: Probability Generating Functions: find the PGF of X + Y where Y has PGF 0.4 + 0.6t. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

Write your answer first, then mark it.

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4. Further Statistics 1: Chi-Squared Tests

6. Further Statistics 2: Linear Regression

Key learning objectives

Understand the key principles behind Further Statistics 1: Probability Generating Functions.
Apply these ideas to exam-style questions.
Recall the essential definitions and key terms.