A discrete random variable gives the number of passengers boarding a bus during a 12-minute interval, with probability distribution shown below:
| 0 | 1 | 2 | 3 | 4 | |
|---|---|---|---|---|---|
| 0.1 | 0.3 | 0.2 |
A voucher value (in dollars) is determined by the formula (so the voucher increases by for each extra passenger).
A discrete random variable represents the number of successful attempts in a sequence of 5 independent trials, each with a success probability of 0.3. The probability distribution of follows a binomial distribution.
Write down the probability mass function of .
A discrete random variable represents the number of errors in a code block, with probability distribution given in the following table:
A continuous random variable has the probability density function:
A discrete random variable takes values in the set , with probability mass function , where is a constant.
Practice IB Mathematics Analysis and Approaches (AA) Topic AHL 4.14—properties of Discrete and Continuous Random Variables with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 4.14—properties of Discrete and Continuous Random Variables and mirrors Paper 1, 2, 3 style where relevant.
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the value of , in dollars.
Hence, the probability distribution for .
the expected value .
Find the variance .
| 0 | 1 | 2 | 3 |
|---|
| 0.4 | 0.3 | 0.1 |
Given that .
Write down an equation for in terms of .
Verify that is a valid probability density function.
Find the cumulative distribution function .
Show that .
A new random variable is defined by .
Find:
(i) ;
(ii) .
The procedure of observing is repeated times independently. Let denote the number of trials in which .
Find the smallest value of such that .
