DP Further Mathematics HL Questionbank

• Syllabus

3.2

Sub sections and their related questions

Linear transformation of a single random variable.

• SPNone.1.hl.TZ0.4a: The shopkeeper places \(100\) randomly chosen potatoes on a weighing machine. Find the...
• SPNone.1.hl.TZ0.4b: Find the minimum number of randomly selected potatoes which are needed to ensure that their total...
• 18M.2.hl.TZ0.1a: Write down the distribution of aX + bY where a, b \( \in \mathbb{R}\).
• 18M.2.hl.TZ0.1b.i: P(X1 + Y1 < 11).
• 18M.2.hl.TZ0.1b.ii: P(3X1 + 4Y1 > 15).
• 18M.2.hl.TZ0.1c: Given that \({\bar X}\) and \({\bar Y}\) are the respective sample means,...
• 18M.2.hl.TZ0.1b.iii: P(X1 + X2 + Y1 + Y2 + Y3 + Y4 < 30).

Mean of linear combinations of n random variables.

• 15M.1.hl.TZ0.7a: Sami is undertaking market research on packets of soap powder. He considers the brand “Gleam”....
• 15M.1.hl.TZ0.7b: Sami now considers the brand “Bright”. The weight of the contents of a randomly chosen packet of...
• 16M.1.hl.TZ0.2a: Find \({\text{P}}\left( {B > {\text{E}}(B) + \frac{1}{2}\sqrt {{\text{Var}}(B)} } \right)\).
• 16M.1.hl.TZ0.2b: Find the probability that the total lifetime of 7 randomly chosen basic vacuum cleaners is less...
• 16M.1.hl.TZ0.2c: Find the probability that the total lifetime of 5 randomly chosen robust vacuum cleaners is...
• 18M.2.hl.TZ0.1a: Write down the distribution of aX + bY where a, b \( \in \mathbb{R}\).
• 18M.2.hl.TZ0.1b.i: P(X1 + Y1 < 11).
• 18M.2.hl.TZ0.1b.ii: P(3X1 + 4Y1 > 15).
• 18M.2.hl.TZ0.1c: Given that \({\bar X}\) and \({\bar Y}\) are the respective sample means,...
• 18M.2.hl.TZ0.1b.iii: P(X1 + X2 + Y1 + Y2 + Y3 + Y4 < 30).

Variance of linear combinations of n independent random variables.

• 15M.1.hl.TZ0.7a: Sami is undertaking market research on packets of soap powder. He considers the brand “Gleam”....
• 15M.1.hl.TZ0.7b: Sami now considers the brand “Bright”. The weight of the contents of a randomly chosen packet of...
• 18M.2.hl.TZ0.1a: Write down the distribution of aX + bY where a, b \( \in \mathbb{R}\).
• 18M.2.hl.TZ0.1b.i: P(X1 + Y1 < 11).
• 18M.2.hl.TZ0.1b.ii: P(3X1 + 4Y1 > 15).
• 18M.2.hl.TZ0.1c: Given that \({\bar X}\) and \({\bar Y}\) are the respective sample means,...
• 18M.2.hl.TZ0.1b.iii: P(X1 + X2 + Y1 + Y2 + Y3 + Y4 < 30).

Expectation of the product of independent random variables.

• 18M.2.hl.TZ0.1a: Write down the distribution of aX + bY where a, b \( \in \mathbb{R}\).
• 18M.2.hl.TZ0.1b.i: P(X1 + Y1 < 11).
• 18M.2.hl.TZ0.1b.ii: P(3X1 + 4Y1 > 15).
• 18M.2.hl.TZ0.1c: Given that \({\bar X}\) and \({\bar Y}\) are the respective sample means,...
• 18M.2.hl.TZ0.1b.iii: P(X1 + X2 + Y1 + Y2 + Y3 + Y4 < 30).