IB Maths AA SL 4.7 Discrete Random Variables Questions

Practise interpreting discrete probability distributions, calculating expected value and mean, and using E(X) = 0 to analyse a fair-game context.

Exam points

Represent a discrete random variable with its probability distribution, checking that outcomes are exhaustive and probabilities sum to one.
Calculate and interpret the expected value E(X), including E(X) = 0 as a fair-game condition, and use it to evaluate a stated context.

[Maximum number: 5]

A supermarket analyses the shopping habits of its customers.
The number of times, X, each customer visits the supermarket in a week is given by the following probability distribution.

Table for Question IB Maths AA SL 4.7 Discrete Random Variables Questions question 1 — IB Maths AA SL

(a)

Find the value of a.

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summing probabilities and equating to 1

\begin{aligned} & 1.5 a+2 a+0.281+a+0.026=1 \\ & (a=) 0.154 \end{aligned}

(b)

Find the mean of X.

The manager wants to know why customers come to their supermarket. They survey the first 50 customers to arrive at the supermarket on a particular day.

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IB Maths AA SL 4.7 Discrete Random Variables Questions question 1

Question (a)

Question (b)