Discrete Random Variables

On this page we will explore the concept of discrete random variables and their probability distributions. We will look at how we can display probability distributions in tables or as functions. The questions are not so complicated (it is just a way of formalising the language of probability), for example, it is important not to forget that probabilities still add up to 1!


Key Concepts

On this page, you should learn about

  • discrete random variables
  • probability distributions
  • mean (expected value)
  • variance (HL only)

Summary

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Test Yourself

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Exam-style Questions

Question 1

 

The discrete random variable X has probability function

 P(X = x) = k(16 – x²) for x = 0, 1, 2, 3

  1. Find the value of the constant k
  2. Find P(1 ≤ X < 3)

Hint

Full Solution

Question 2

 

The random variable X has probability function

a) Find the value of k

b) Work out \(P(X\ge 2)\)

Hint

Full Solution

Question 3

    

Two boxes each contain three cards. 

The first box contains cards labelled 1,3 and 5

The second box contains cards labelled 2, 4 and 6. 

In a game, a player draws one card at random from each box and his score, X, is the sum of the numbers on the two cards.

a) Complete the following probability distribution

b) Work out E(X)

Hint

Full Solution

Question 4

 

The following table shows the probability distribution of a discrete random variable X

If X represents the return from a game. Find a and b if the game is fair.

Hint

Full Solution

 

Question 5

 

The discrete random variable X has probability function

\(P(X=x)=k(\frac{2}{5})^x\) , for \(x\in Z ,\quad x>0\)

Work out the value of k

Hint

Full Solution

 

 

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