(Solved): 1. Laptops In a store, two customers ask a salesman advice about laptops. The first customer will pu ...

1. Laptops In a store, two customers ask a salesman advice about laptops. The first customer will purchase a laptop with probability 0.3 , and independently of the first customer, the second will buy a laptop with probability 0.6 . Any sale made is equally likely to be either for model A, which costs \( \$ 1000 \), or model B, which costs \( \$ 500 \). Let \( X \) be the total dollar value of all sales. (a) Determine the probability mass function of \( X \). (b) Determine the expected value of \( X \), and interpret it in the context of the problem. (c) Compute the variance and the standard deviation of \( X \). Include units in your solution.