Determine and use the mean (expected value) of a discrete random variable as a measurement of centre, 𝐸(𝑋) = 𝜇 = ∑ 𝑝𝑖 𝑥𝑖 where 𝑝𝑖 is the probability of outcome 𝑥𝑖 occurring.

A telecommunications company monitors the number of network outages per week across its regional centres. The probability distribution for the number of outages per week, \(X\), is shown in the table below. The company incurs a cost of $\$8{,}000$ per outage for emergency repairs, plus a fixed weekly monitoring cost of $\$12{,}000$ regardless of the number of outages. Determine the expected weekly total cost, in dollars, that the company will incur.

A discrete random variable $X$ represents the number of faulty items in a batch of 10 products. The probability distribution is given in the table below. Determine the expected number of faulty items.

A discrete random variable X has the probability distribution shown below. Calculate the expected value E(X).

A local café tracks the number of takeaway coffees sold per customer during morning peak hour. The probability distribution is shown in the table below. Determine the expected number of coffees sold per customer.