Question
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Answer
The expected value of
is $10.93, with a variance of 210.73 and a standard deviation of approximately $14.52.
Solution
It looks like you’ve provided a probability distribution table for a discrete random variable
. Let’s interpret the table and perform some useful calculations, such as finding the expected value and variance of
.
Given Probability Distribution
- Possible Outcomes (
): $100, $75, $8 - Probabilities (
): 0.01, 0.03, 0.96 respectively
1. Expected Value (
)
The expected value is a measure of the central tendency of the distribution. It represents the average outcome if the experiment is repeated many times.
Calculating each term:
Adding them up:
Interpretation: On average, the expected value of
is $10.93.
2. Variance (
) and Standard Deviation (
)
Variance measures the spread of the distribution around the expected value.
First, compute
:
Calculating each term:
Adding them up:
Now, calculate the variance:
The standard deviation is the square root of the variance:
Interpretation:
- Variance: 210.73
- Standard Deviation: Approximately 14.52
3. Summary
- Expected Value (
): $10.93 - Variance (
): 210.73 - Standard Deviation (
): $14.52
If you have a specific question or need further analysis related to this distribution, feel free to ask!
Answered by UpStudy AI and reviewed by a Professional Tutor
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Extra Insights
Did you know that the data you’re looking at represents a probability distribution? In this setup,
has three possible outcomes: $100, $75, and $8, with their respective probabilities. This kind of model is commonly used in finance to evaluate investment options or in gambling to calculate the odds of winning. Understanding these probabilities can help you make smarter decisions, whether you’re playing a game or investing your money!
To make the most of such models, it’s crucial to avoid common pitfalls. One major mistake is ignoring the expected value calculation. You can find the expected value by multiplying each outcome by its probability and adding them all up. This gives you a clearer idea of what to expect in terms of return. Not understanding the importance of probabilities can lead you to take unwanted risks, so always calculate before diving in!