# Question: During the course of a day a machine turns out

During the course of a day a machine turns out two items, one in the morning and one in the afternoon. The quality of each item is measured as good (G), mediocre (M), or bad (B). The longrun fraction of good items the machine produces is 1 2, the fraction of mediocre items is 1 3, and the fraction of bad items is 1 6.

(a) In a column, write the sample space for the experiment that consists of observing the day’s production.

(b) Assume a good item returns a profit of $2, a mediocre item a profit of $1, and a bad item yields nothing. Let X be the random variable describing the total profit for the day. In a column adjacent to the column in part (a), write the value of this random variable corresponding to each point in the sample space.

(c) Assuming that the qualities of the morning and afternoon items are independent, in a third column associate with every point in the sample space a probability for that point.

(d) Write the set of all possible outcomes for the random variable X. Give the probability distribution function for the random variable.

(e) What is the expected value of the day’s profit?

(a) In a column, write the sample space for the experiment that consists of observing the day’s production.

(b) Assume a good item returns a profit of $2, a mediocre item a profit of $1, and a bad item yields nothing. Let X be the random variable describing the total profit for the day. In a column adjacent to the column in part (a), write the value of this random variable corresponding to each point in the sample space.

(c) Assuming that the qualities of the morning and afternoon items are independent, in a third column associate with every point in the sample space a probability for that point.

(d) Write the set of all possible outcomes for the random variable X. Give the probability distribution function for the random variable.

(e) What is the expected value of the day’s profit?

## Relevant Questions

The random variable X has density function f given by (a) Determine K in terms of θ. (b) Find FX(b), the CDF of X. (c) Find E(X). (d) Suppose The distribution of X, the life of a transistor, in hours, is approximated by a triangular distribution as follows: (a) What is the value of a? (b) Find the expected value of the life of transistors. (c) Find the CDF, FX(b), ...Consider a parallel system consisting of two independent components whose time to failure distributions are exponential with parameters μ1 and μ2, respectively (μ1 ≠ μ2). Show that the time to failure distribution of ...Follow the instructions of Prob. 25.4-1 when using the following network. Note that component 3 flows in both directions. (a) Find all the minimal paths and cuts. (b) Compute the exact system reliability, and evaluate it ...A certain queueing system has a Poisson input, with a mean arrival rate of 4 customers per hour. The service-time distribution is exponential, with a mean of 0.2 hour. The marginal cost of providing each server is $20 per ...Post your question