IBMathsDPAnalysis & Approaches (AA)HLExam Questions4. Statistics & ProbabilityDiscrete Random Variables

Discrete Random Variables (DP IB Analysis & Approaches (AA): HL): Exam Questions

4 hours37 questions

6 marks

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

$x$	0	1	2	3	4
$P (X = x)$	$\frac{5}{24}$	$\frac{1}{3}$	$\frac{1}{4}$	$\frac{1}{12}$	$\frac{1}{8}$

Find

(i) $P (X < 4)$

(ii) $P (X > 1)$

(iii) $P (2 < X \leq 4)$

(iv) $P (0 < X < 4)$ .

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$x$	0	1	2	3	4	5	6
$P (X = x)$	$a$	$2 a$	$3 a$	$4 a$	$5 a$	$6 a$	$7 a$

Number on sector	0	1	1	2	3	5
Probability	$\frac{6}{20}$	$p$	$\frac{3}{20}$	$\frac{5}{20}$	$\frac{3}{20}$	$\frac{1}{20}$

$x$	$- 3$	$- 1$	0	1	3
$P (X = x)$	0.11	$k^{2}$	0.1	$2 k$	0.1

Section	A	B	C	D	E
Probability	0.55	0.15	0.15	0.1	0.05

Section	A	B	C	D	E
Points	$- 5$	2	3	10	$k$

Score, $x$	1	2	3	4	5	6
$P (X = x)$	$\frac{1}{6}$	$\frac{1}{2} p$	$\frac{1}{8}$	$\frac{3}{2} p$	$\frac{1}{12}$	$3 p$

Region	A	B	C	Missed target
Probability	$\frac{1}{15}$	$\frac{2}{15}$	$\frac{a}{15}$	$\frac{b}{15}$

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

$x$	0	1	2	3	4	5	6	7	8
$P (X = x)$	0.32	0.22	0.21	$\frac{1}{k}$	$\frac{7}{k^{2}}$	$\frac{4}{k^{2}}$	$\frac{2}{k^{2}}$	$\frac{1}{k^{2}}$	$\frac{1}{k^{2}}$

$x$	0	1	2	3	4	5	6	7	8
$P (X = x)$	0.1925	0.1815	0.2250	$p$	0.0895	0.0504	0.0307	0.0104	$q$

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

Number on sector	1	2	3	4	5	6
Probability	$1.5 p$	$p$	$\frac{3}{25}$	$\frac{1}{10}$	$\frac{3}{50}$	$\frac{1}{100}$

Prize, $s$	0	2	10	20	100	Grand prize
$P (S = s)$	$\frac{1}{2}$	$\frac{1}{4}$	$\frac{1}{6}$	$\frac{1}{24}$	$p$	$\frac{1}{1000}$

$x$	$- 5$	$- 3$	$- 1$	0	1	3	5
$P (X = x)$	0.24	$2 k^{2}$	0.04	0.12	$3 k$	0.19	0.11

$y$
$P (Y = y)$

$y$	$- 10$	$- 6$	$- 3$	$- 2$	1	4	5	8	12
$P (Y = y)$

Number of strokes, $x$	70	71	72	75	76	78	80
Frequency	1	7	10	3	2	1	1

Score, $x$	$- 4$	$- 2$	$- 1$	0	1	3	5	6
$P (X = x)$	$\frac{1}{6}$	$p$	$\frac{1}{8}$	$\frac{1}{4}$	$\frac{1}{12}$	$\frac{1}{8}$	$\frac{1}{48}$	$q$