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

1a

2 marks

A continuous random variable $X$ has the probability density function given by

$f (x) = \{\begin{cases} k \sin 2 x, & 0 \leq x \leq \frac{π}{3} \\ 0, & otherwise \end{cases}$

Find the value of $k$ .

How did you do?

1b

3 marks

Giving your answers to three significant figures, find

(i)

the mean of

X

,

(ii)

the mode of

X

.

How did you do?

1c

2 marks

(i)

Write down

P (X = \frac{π}{3})

(ii)

Show that the median,

m

, of

X

lies in the interval

\frac{π}{6} < m < \frac{π}{3}

.

How did you do?

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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 $k$ .

How did you do?

1b

2 marks

Find $E (X) .$

How did you do?

1c

2 marks

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

How did you do?

1d

3 marks

Find $Var (X) .$

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1a

3 marks

The continuous random variable $X$ has the probability density function

$f (x) = \{\begin{cases} k e x, & 0 \leq x \leq a \\ k (e^{2} - e^{x}), & a \leq x \leq 2 \\ 0, & otherwise \end{cases}$

where $a$ and $k$ are constants.

Given that $f$ is a continuous function, find the values of $a$ and $k$ .

How did you do?

1b

5 marks

(i)

Find

P (0.5 \leq X \leq 1.5)

(ii)

Find

P (X > 1)

How did you do?

1c

3 marks

Find the median of $X$ .

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Medium
Hard
Very Hard

$x$	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
$P (B = b)$

DP IB Maths: AA HL

Topic Questions

4.7 Further Probability Distributions