During the course of a day a machine turns out two items, one in the morning and

Question

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 long run fraction of good items the machine produces is 12, the fraction of mediocre items is 13, and the fraction of bad items is 16.

(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 a probability for every point in the sample space.

(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?

(f) Calculate the standard deviation of the day’s profit.

I NEED YOUR WORK NOT COPY AND PASTE

Tybing please

Explanation / Answer

a) The sample space for the experiment that consists of observing the day's production is given as:

b) A good item returns a profit of $2, a mediocre item a profit of $1, and a bad item yields nothing, the random variable Profit is depicted in the second column as:

c) As the qualities of the morning and afternoon items are independent, the probabilities for each of the 9 instances is computed as:

d) Now the probability distribution of X from the above table is given as:

This is the required PDF for X.

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