Question

A probability distribution for a random variable X is given byP(X=x)=cx, for x=1,2,3,4and c is a constant. Find E(X), the expected value of X.

Answer 1

The Solution.

The given probability distribution is

$P(X=x)=cx,x=1,2,3,4$

The expected value for the random variable X is given by the formula below:

$\begin{gathered} E(X)=\sum ^4_{x\mathop=1}xP(x) \\ \text{where P(x)=cx} \end{gathered}$

This implies that:

$E(X)=1.P(1)+2.P(2)+3.P(3)+4.P(4)$$E(X)=1(c)+2(2c)+3(3c)+4(4c)$$E(X)=c+4c+9c+16c=30c$

So, the expected value of X is 30c.

Thus, the correct answer is 30c.