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The table below shows the probability distribution of a random variable X. X P(X) --20 0.39 -19 0.02 -18 0.18 0.22 -16 0.1 -15 0.09 What is the mean of the probability distribution? Write your answer as a decimal.

User Oprimus
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1 Answer

2 votes

ANSWER

-18.11

Step-by-step explanation

We want to find the mean of the probability distribution.

To do that, we apply the formula:


\mu=\Sigma\mleft\lbrace X\cdot P(X)\mright\rbrace

This means that we have to find the product of each value has its corresonding probability and find the sum:


\begin{gathered} \mu=(-20\cdot0.39)+(-19\cdot0.02)+(-18\cdot0.18)+(-17\cdot0.22)+(-16\cdot0.1)+(-15\cdot0.09) \\ \mu=(-7.8)+(-0.38)+(-3.24)+(-3.74)+(-1.6)+(-1.35) \\ \mu=-18.11 \end{gathered}

That is the mean of the probability distribution.

User Jhole
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