Question

If X assumes value of $1.2$ and $5$ with the probability of $0.2,0.35$ and $0.45$ respectively. What is the expected value of X

• A. $3.20$
• B. $3.15$
• C. $.80$
• D. $3.25$

Answer 1

The correct option is B $3.15$

According to the question, the probability distribution of variable X can be written as:

X	1	2	5
P(X)	0.2	0.35	0.45

The expected value of X is nothing but the mean of X, i.e., $\mu$

Hence, $\mu =E\left(X\right)={\sum }_{i=1}^n{x}_i{p}_i$

$\mu =1\times 0.2+2\times 0.35+5\times 0.45=0.2+0.7+2.25=3.15$