Question

The table below shows the probability distribution of a random variable X. X P(X) -20 0.53 -19 0.11 -18 0.26 -17 0.09 -16 0.01 What is the expected value of X? Write your answer as a decimal.

Answer 1

ANSWER

$E(X)=-19.06$

EXPLANATION

We want to find the expected value of x.

To do this, we need to find the product of each value with its corresponding proabibilty and then find the sum.

That is:

$E(x)=\Sigma\mleft\lbrace xP(x)\mright\rbrace$

Therefore, we have:

$\begin{gathered} E(X)=(-20\cdot0.53)+(-19\cdot0.11)+(-18\cdot0.26)+(-17\cdot0.09)+(-16\cdot0.01)_{} \\ E(X)=(-10.6)+(-2.09)+(-4.68)+(-1.53)+(-0.16) \\ E(X)=-19.06 \end{gathered}$

That is the expected value.