Further Probability Distributions | DP IB Maths: AA HL Topic Questions 2021

1a

3 marks

A ‘lucky dip’ bag contains seven bars of chocolate and 5 packets of sweets. Suraya selects two items at random without replacing them.

The probability distribution table for the discrete random variable $X$ , “the number of packets of sweets selected”, is shown below.

$X$	0	1	2
$P (X = x)$	$\frac{21}{66}$	$\frac{7 k}{66}$	$\frac{2 k}{66}$

Find the value of $k$ .

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1b

2 marks

Find $E (X) .$

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1c

2 marks

Find $E (X^{2})$ .

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1d

3 marks

Find $Var (X) .$

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$x$	1	2	3	4	5	6	7	8	9
$P (X = x)$	$\frac{k - 1}{27}$	$\frac{k}{27}$	$\frac{k + 1}{27}$	$\frac{k - 1}{27}$	$\frac{k}{27}$	$\frac{k + 1}{27}$	$\frac{k - 1}{27}$	$\frac{k}{27}$	$\frac{k + 1}{27}$

B	5	6	7
$P (B = b)$

Further Probability Distributions (DP IB Maths: AA HL)