DP Mathematics HL Questionbank

• Syllabus

5.5

Sub sections and their related questions

Concept of discrete and continuous random variables and their probability distributions.

• 12M.2.hl.TZ1.2: The probability density function of the continuous random variable X is given by...
• 12M.2.hl.TZ2.7a: Find the value of a .
• 12M.3sp.hl.TZ0.4a: Sketch the function f and show that the lower quartile is 0.5.
• 12M.3sp.hl.TZ0.4b: (i)     Determine E(X ). (ii)     Determine \({\text{E}}({X^2})\).
• 08M.1.hl.TZ1.9: The random variable T has the probability density...
• 08M.1.hl.TZ2.1: The probability distribution of a discrete random variable X is defined...
• 08N.1.hl.TZ0.8: John removes the labels from three cans of tomato soup and two cans of chicken soup in order to...
• 11M.1.hl.TZ2.3b: Find the value of k .
• SPNone.1.hl.TZ0.4a: Determine \({\text{E}}(X)\) .
• SPNone.1.hl.TZ0.4b: Determine the mode of X .
• 10M.2.hl.TZ2.2: A discrete random variable X has a probability distribution given in the following...
• 10N.2.hl.TZ0.11: Tim throws two identical fair dice simultaneously. Each die has six faces: two faces numbered 1,...
• 13M.2.hl.TZ2.7a: Show that a = 9.6.
• 13M.2.hl.TZ2.7b: Sketch the graph of the distribution.
• 13M.2.hl.TZ2.7c: Find \({\text{P}}(X < 0.6)\).
• 13M.2.hl.TZ2.9b: Over a weekend of two days, it is given that a total of three requests are received. Find the...
• 11N.1.hl.TZ0.10a: Find the value of k.
• 13N.1.hl.TZ0.2: The discrete random variable X has probability distribution:   (a)     Find the value of...
• 13N.2.hl.TZ0.11b: A continuous random variable \(X\) has probability distribution function \(f\) given by     ...
• 15N.2.hl.TZ0.8a: Find the value of \(A\) to three decimal places.
• 16M.2.hl.TZ2.10a: Sketch the graph of \(y = f(t)\).
• 16M.2.hl.TZ2.10b: Use your sketch to find the mode of \(T\).
• 16M.2.hl.TZ2.10c: Find the mean of \(T\).
• 16M.2.hl.TZ2.10d: Find the variance of \(T\).
• 16M.2.hl.TZ2.10e: Find the probability that \(T\) lies between the mean and the mode.
• 16M.2.hl.TZ2.10f: (i)     Find \(\int_0^\pi  {f(t){\text{d}}t} \) where \(0 \leqslant T \leqslant \frac{\pi...
• 16N.1.hl.TZ0.1: Find the coordinates of the point of intersection of the planes defined by the equations...
• 16N.1.hl.TZ0.2a: Complete the probability distribution table for \(X\).
• 16N.1.hl.TZ0.2b: Find the expected value of \(X\).
• 16N.2.hl.TZ0.1a: Determine the value of \({\text{E}}({X^2})\).
• 16N.2.hl.TZ0.1b: Find the value of \({\text{Var}}(X)\).
• 18M.1.hl.TZ1.3a: Find the value of a and the value of b.
• 18M.1.hl.TZ1.3b: Find the expected value of T.
• 18M.2.hl.TZ1.10a: Show that \(a = \frac{2}{3}\).
• 18M.2.hl.TZ1.10b: Find \({\text{P}}\left( {X < 1} \right)\).
• 18M.2.hl.TZ1.10c: Given that...

Definition and use of probability density functions.

• 12M.2.hl.TZ1.2: The probability density function of the continuous random variable X is given by...
• 12M.2.hl.TZ2.7a: Find the value of a .
• 12N.1.hl.TZ0.5a: State the mode of X .
• 12N.1.hl.TZ0.5b: Determine the value of a .
• 12N.1.hl.TZ0.5c: Find E(X ) .
• 08M.2.hl.TZ2.4: A continuous random variable X has probability density...
• 08N.2.hl.TZ0.3: A continuous random variable X has a probability density function given...
• 09M.1.hl.TZ2.3: A random variable has a probability density function given...
• SPNone.1.hl.TZ0.4a: Determine \({\text{E}}(X)\) .
• SPNone.1.hl.TZ0.4b: Determine the mode of X .
• 13M.1.hl.TZ1.4: The probability density function of the random variable X is defined...
• 10M.3sp.hl.TZ0.3a: The random variable X is assumed to have probability density function f,...
• 10M.1.hl.TZ1.12: A continuous random variable X has probability density...
• 10M.1.hl.TZ2.1: A continuous random variable X has the probability density function f given...
• 09N.2.hl.TZ0.5: The annual weather-related loss of an insurance company is modelled by a random variable \(X\)...
• 14M.2.hl.TZ1.11: A random variable \(X\) has probability density...
• 14M.2.hl.TZ2.11: The probability density function of a random variable X is defined...
• 13N.1.hl.TZ0.2: The discrete random variable X has probability distribution:   (a)     Find the value of...
• 14N.1.hl.TZ0.9b: Find the interquartile range of \(T\).
• 14N.3sp.hl.TZ0.1a: Sketch the graph of \(y = f(x)\).
• 15M.2.hl.TZ1.11a: Sketch the graph \(y = f(x)\).
• 15M.2.hl.TZ1.11b: Find \({\text{P}}(X \le \pi )\).
• 15M.2.hl.TZ1.11c: Show that \(a = \frac{1}{{{\pi ^2}}}\).
• 15M.2.hl.TZ1.11g: Find \({\text{P}}\left( {\frac{\pi }{2} \le X \le \frac{{3\pi }}{2}} \right)\).
• 15M.2.hl.TZ1.11h: Given that \(\frac{\pi }{2} \le X \le \frac{{3\pi }}{2}\) find the probability that...
• 15N.2.hl.TZ0.8a: Find the value of \(A\) to three decimal places.

Expected value (mean), mode, median, variance and standard deviation.

• 12M.2.hl.TZ1.2: The probability density function of the continuous random variable X is given by...
• 12M.2.hl.TZ1.7: A fisherman notices that in any hour of fishing, he is equally likely to catch exactly two fish,...
• 12M.1.hl.TZ2.11e: Using this probability distribution, calculate the mean of X .
• 12M.2.hl.TZ2.7b: Find the mean of X .
• 12N.1.hl.TZ0.5a: State the mode of X .
• 12N.1.hl.TZ0.5b: Determine the value of a .
• 12N.1.hl.TZ0.5c: Find E(X ) .
• 08M.1.hl.TZ2.1: The probability distribution of a discrete random variable X is defined...
• 08N.1.hl.TZ0.8: John removes the labels from three cans of tomato soup and two cans of chicken soup in order to...
• 08N.2.hl.TZ0.3: A continuous random variable X has a probability density function given...
• 11M.2.hl.TZ2.12d: To encourage safety the factory pays a bonus of $1000 into a fund for workers if no accidents...
• 09M.1.hl.TZ2.3: A random variable has a probability density function given...
• SPNone.1.hl.TZ0.4a: Determine \({\text{E}}(X)\) .
• SPNone.1.hl.TZ0.4b: Determine the mode of X .
• SPNone.3sp.hl.TZ0.5a: Determine \({\text{E}}(X)\) and show that \({\text{Var}}(X) = 6\theta - 16{\theta ^2}\).
• 10M.1.hl.TZ1.12: A continuous random variable X has probability density...
• 10M.1.hl.TZ2.1: A continuous random variable X has the probability density function f given...
• 10N.2.hl.TZ0.11: Tim throws two identical fair dice simultaneously. Each die has six faces: two faces numbered 1,...
• 11N.1.hl.TZ0.10b: Find \({\text{E}}(X)\).
• 11N.1.hl.TZ0.10c: Find the median of X.
• 09N.2.hl.TZ0.5: The annual weather-related loss of an insurance company is modelled by a random variable \(X\)...
• 14M.1.hl.TZ1.2: Four numbers are such that their mean is 13, their median is 14 and their mode is 15. Find the...
• 14M.2.hl.TZ1.11: A random variable \(X\) has probability density...
• 14M.2.hl.TZ2.11: The probability density function of a random variable X is defined...
• 13N.1.hl.TZ0.2: The discrete random variable X has probability distribution:   (a)     Find the value of...
• 15M.2.hl.TZ1.11d: Write down the median of \(X\).
• 15M.2.hl.TZ1.11e: Calculate the mean of \(X\).
• 15M.2.hl.TZ1.11f: Calculate the variance of \(X\).
• 15N.2.hl.TZ0.8b: Find the mode of \(X\).

Applications.

• 12M.2.hl.TZ1.7: A fisherman notices that in any hour of fishing, he is equally likely to catch exactly two fish,...
• 12M.2.hl.TZ2.7b: Find the mean of X .