DP Mathematics HL Questionbank

• Syllabus

7.2

Sub sections and their related questions

Linear transformation of a single random variable.

• 12M.3sp.hl.TZ0.4c: Two independent observations are made from X and the values are added. The resulting random...
• 12N.3sp.hl.TZ0.2a: Find the mean and the variance of (i)     \({X_1} + {X_2}\) ; (ii)     \(3{X_1}\); (iii)    ...
• 12N.3sp.hl.TZ0.2b: Find \({\text{E}}(X_1^2)\) in terms of \(\mu \) and \(\sigma \) .
• 08M.3sp.hl.TZ2.1a: The random variable Y is such that \({\text{E}}(2Y + 3) = 6{\text{ and Var}}(2 - 3Y) =...
• 11M.3sp.hl.TZ0.1b: Five of these oranges are selected at random to be put into a bag. Find the probability that the...
• 11M.3sp.hl.TZ0.1c: The farm also produces lemons whose weights may be assumed to be normally distributed with mean...
• 11N.3sp.hl.TZ0.1c: Find the probability that five randomly chosen Supermug tea bags contain a total of less than...
• 11N.3sp.hl.TZ0.1d: Find the probability that the total weight of tea in seven randomly chosen Supermug tea bags is...
• 14M.3sp.hl.TZ0.1b: \(\bar X\) denotes the sample mean of \(n > 1\) independent observations from \(X\). (i)    ...
• 13N.3sp.hl.TZ0.5: Let \(X\) and \(Y\) be independent random variables with \(X \sim {P_o}{\text{ (3)}}\) and...
• 18M.3sp.hl.TZ0.1a: Find the probability that a randomly chosen male bird weighs between 4.75 kg and 4.85 kg.
• 18M.3sp.hl.TZ0.1b: Find the probability that the weight of a randomly chosen male bird is more than twice the weight...
• 18M.3sp.hl.TZ0.1c: Two randomly chosen male birds and three randomly chosen female birds are placed on a weighing...

Mean of linear combinations of \(n\) random variables.

• 08M.3sp.hl.TZ1.5: (a)     Having thrown the die once, she lets \({X_2}\) denote the number of additional throws...
• 08M.3sp.hl.TZ2.1b: Independent random variables R and S are such...
• 08N.3sp.hl.TZ0.4: (a)     A random variable, X , has probability density function defined...
• 14N.3sp.hl.TZ0.4b: \(Y\) is a random variable, independent of \(X\), that also follows a Poisson distribution with...
• 15M.3sp.hl.TZ0.1b: A large can and a small can are selected at random. Find the probability that the large can...
• 15M.3sp.hl.TZ0.1c: A large can and five small cans are selected at random. Find the probability that the large can...
• 15N.3sp.hl.TZ0.3: Two students are selected at random from a large school with equal numbers of boys and girls. The...
• 16M.3sp.hl.TZ0.1a: Given that, on a randomly chosen day, the probability that he completes the crossword in less...
• 16M.3sp.hl.TZ0.1b: Find the probability that the total time taken for him to complete five randomly chosen...
• 16M.3sp.hl.TZ0.1c: Find the probability that, on a randomly chosen day, the time taken by Beatrice to complete the...
• 16N.3sp.hl.TZ0.3a: (i)     State the distribution of \(X\), including its parameters. (ii)     Calculate...
• 16N.3sp.hl.TZ0.3b: (i)     Calculate \({\text{E}}(Y)\). (ii)     Calculate \({\text{P}}(Y = 5)\).
• 18M.3sp.hl.TZ0.1a: Find the probability that a randomly chosen male bird weighs between 4.75 kg and 4.85 kg.
• 18M.3sp.hl.TZ0.1b: Find the probability that the weight of a randomly chosen male bird is more than twice the weight...
• 18M.3sp.hl.TZ0.1c: Two randomly chosen male birds and three randomly chosen female birds are placed on a weighing...

Variance of linear combinations of \(n\) independent random variables.

• 08M.3sp.hl.TZ2.1b: Independent random variables R and S are such...
• 08N.3sp.hl.TZ0.4: (a)     A random variable, X , has probability density function defined...
• 14N.3sp.hl.TZ0.4b: \(Y\) is a random variable, independent of \(X\), that also follows a Poisson distribution with...
• 15M.3sp.hl.TZ0.1b: A large can and a small can are selected at random. Find the probability that the large can...
• 15M.3sp.hl.TZ0.1c: A large can and five small cans are selected at random. Find the probability that the large can...
• 15N.3sp.hl.TZ0.3: Two students are selected at random from a large school with equal numbers of boys and girls. The...
• 16M.3sp.hl.TZ0.1a: Given that, on a randomly chosen day, the probability that he completes the crossword in less...
• 16M.3sp.hl.TZ0.1b: Find the probability that the total time taken for him to complete five randomly chosen...
• 16M.3sp.hl.TZ0.1c: Find the probability that, on a randomly chosen day, the time taken by Beatrice to complete the...
• 18M.3sp.hl.TZ0.1a: Find the probability that a randomly chosen male bird weighs between 4.75 kg and 4.85 kg.
• 18M.3sp.hl.TZ0.1b: Find the probability that the weight of a randomly chosen male bird is more than twice the weight...
• 18M.3sp.hl.TZ0.1c: Two randomly chosen male birds and three randomly chosen female birds are placed on a weighing...

Expectation of the product of independent random variables.

• 18M.3sp.hl.TZ0.1a: Find the probability that a randomly chosen male bird weighs between 4.75 kg and 4.85 kg.
• 18M.3sp.hl.TZ0.1b: Find the probability that the weight of a randomly chosen male bird is more than twice the weight...
• 18M.3sp.hl.TZ0.1c: Two randomly chosen male birds and three randomly chosen female birds are placed on a weighing...