exercise 1.the probabilities of laptops to have 0, 1, 2, 3 or 4 defective parts are 0.24, 0.18, 0.26, 0.12…

Step1: Recall the formula for the mean of a probability distribution

The formula for the mean (\mu) of a discrete probability distribution is (\mu=\sum_{i}x_ip_i), where (x_i) are the values of the random variable and (p_i) are their corresponding probabilities.

Step2: Calculate each (x_ip_i) term

• For (x = 0) and (p=0.24): (0\times0.24 = 0)
• For (x = 1) and (p = 0.18): (1\times0.18=0.18)
• For (x = 2) and (p = 0.26): (2\times0.26 = 0.52)
• For (x = 3) and (p = 0.12): (3\times0.12=0.36)
• For (x = 4) and (p = 0.20): (4\times0.20 = 0.8)

Step3: Sum up the (x_ip_i) terms

(\mu=0 + 0.18+0.52 + 0.36+0.8) [ \begin{align*} \mu&=(0.18 + 0.52)+(0.36 + 0.8)\ &=0.7+1.16\ &=1.86 \end{align*} ]

Answer:

(1.86)