Linear Combinations of Random Variables (CIE A Level Maths: Probability & Statistics 2)

Exam Questions

4 hours30 questions

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4 marks

The discrete random variable $X$ has the probability distribution shown in the following table.

$x$	0	1	2	3	4
$P (X = x)$	0.1	0.2	0.3	0.2	0.2

(i)

Show that

E (X) = 2.2

(ii)

Show that

V a r (X) = 1.56

How did you do?

1 mark

Complete the row in the table below to show the probability distribution for $X + 5$ .

$x$	0	1	2	3	4
$x + 5$	5
$P (X = x)$	0.1	0.2	0.3	0.2	0.2

How did you do?

2 marks

Use the second and third rows in table in part (b) with the formula $E (X + 5) = \sum (x + 5) p$ to verify that $E (X + 5) = E (X) + 5$ .

How did you do?

2 marks

Use the second and third rows in table in part (b) with the formulae $E (X + 5)^{2} = \sum (x + 5)^{2} p$ and $V a r (X + 5) = E (X + 5)^{2} - (E {(X + 5))}^{2}$ to verify that $V a r (X + 5) = V a r (X)$ .

How did you do?

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