Question 1183259: A disk drive manufacturer sells storage devices with capacities of one terabyte, 500 gigabytes, and 100 gigabytes with probabilities 0.5, 0.3, and 0.2, respectively. The revenues associated with the sales in that year are estimated to be $50 million, $25 million, and $10 million, respectively. Let X denote the revenue of storage devices during that year. Determine the probability mass function of X.
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Here's how to determine the probability mass function (PMF) of X:
1. **Identify the possible values of X:**
X represents the revenue. The possible values of X are $50 million, $25 million, and $10 million.
2. **Assign probabilities to each value of X:**
The probabilities are given in the problem:
* P(X = $50 million) = 0.5
* P(X = $25 million) = 0.3
* P(X = $10 million) = 0.2
3. **Express the PMF:**
The probability mass function of X, denoted as p(x) or P(X=x) is:
```
p(x) =
0.5, if x = $50 million
0.3, if x = $25 million
0.2, if x = $10 million
0, otherwise
```
Or, in a table format:
| x (Revenue in millions) | p(x) |
|---|---|
| 10 | 0.2 |
| 25 | 0.3 |
| 50 | 0.5 |
This PMF completely describes the probabilities associated with each possible revenue value. It tells us, for example, that there's a 50% chance the revenue will be $50 million, a 30% chance it will be $25 million, and a 20% chance it will be $10 million.
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