Question

the following table shows the probability distribution for the number of books a student typically buys at the annual book fair held at an elementary school.

number of books	0	1	2	3	4	5	6	7

let the random variable ( b ) represent the number of books a student buys at the next book fair. what is the expected value of ( b )?

Explanation:

Step1: Recall expected value formula

The expected value $E(B)$ of a discrete random variable is calculated as $E(B) = \sum [b \cdot P(b)]$, where $b$ is the number of books and $P(b)$ is the corresponding probability.

Step2: Calculate each term $b \cdot P(b)$

• $0 \times 0.35 = 0$
• $1 \times 0.20 = 0.20$
• $2 \times 0.15 = 0.30$
• $3 \times 0.10 = 0.30$
• $4 \times 0.07 = 0.28$
• $5 \times 0.08 = 0.40$
• $6 \times 0.04 = 0.24$
• $7 \times 0.01 = 0.07$

Step3: Sum all calculated terms

$0 + 0.20 + 0.30 + 0.30 + 0.28 + 0.40 + 0.24 + 0.07$

Answer:

$1.79$