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Probability

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Question : 127 of 127

Marks: +1, -0

Find the Expected value of the following distribution

X	$-20$	$-10$	$30$	$75$	$80$
P(x)	$\frac{3}{20}$	$\frac{1}{5}$	$\frac{1}{2}$	$\frac{1}{10}$	$\frac{1}{20}$

$20.5$
$21.5$
$22.5$
$24.5$

Solution:

Concept:

Expected value is the sum of each value multiplied by its probability.

Explanation:

Convert all probabilities to denominator 20:

P(-20)=\frac{3}{20}

,

P(-10)=\frac{1}{5}=\frac{4}{20}

,

P(30)=\frac{1}{2}=\frac{10}{20}

,

P(75)=\frac{1}{10}=\frac{2}{20}

,

P(80)=\frac{1}{20}

.

Multiply each

X

by its

P(X)

and add:

(-20)\times\frac{3}{20} = -3

(-10)\times\frac{4}{20} = -2

30\times\frac{10}{20} = 15

75\times\frac{2}{20} = 7.5

80\times\frac{1}{20} = 4

Sum:

-3 -2 +15 +7.5 +4 = 21.5

.

Answer:

21.5

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