Linear Combinations of Random Variables | CIE A Level Maths: Probability & Statistics 2 Exam Questions 2020

1a

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

.

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1b

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?

1c

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?

1d

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 $V a r (X + 5) = V a r (X)$ .

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$s$	1	4	9
$P (S = s)$	0.2	0.5	0.3

$t$	1	3	6	10
$P (T = t)$	0.25	0.25	0.25	0.25

	Mean	Standard Deviation
Rabbit	30	9
Chinchilla	145	20
Degu	37	6

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

Exam Questions

1. Statistical Sampling

1.1 Sampling & Data Collection

1.2 Sampling & Estimation

2. Statistical Distributions

2.1 Poisson Distribution

2.2 Linear Combinations of Random Variables

2.3 Continuous Random Variables

2.4 Working with Distributions

3. Hypothesis Testing

3.1 Hypothesis Testing

3.2 Hypothesis Testing (Discrete Distribution)

3.3 Hypothesis Testing (Normal Distribution)