Math Problem Statement
Solution
It looks like you have an exercise on probability distribution, where you need to complete the table and calculate the mean. From the table, I can see values for and their corresponding probabilities , along with some of the missing entries.
Let’s complete the table first:
The table currently looks like this:
\hline X & P(X) & X \cdot P(X) \\ \hline 0 & 0.1 & 0 \\ 1 & 0.15 & 1 \cdot 0.15 = 0.15 \\ 2 & 0.4 & 2 \cdot 0.4 = 0.8 \\ 3 & 0.35 & 3 \cdot 0.35 = 1.05 \\ \hline \end{array}$$ For the missing value in the table, it appears that the total sum of probabilities is 1. Therefore, we can calculate the remaining probability. To check: $$P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.1 + 0.15 + 0.4 + 0.35 = 1.0$$ It seems the probabilities are correctly assigned. Next, to calculate the mean ($$\mu$$), we can use the formula: $$\mu = \sum (X \cdot P(X)) = 0 + 0.15 + 0.8 + 1.05 = 2$$ This confirms the mean is $$\mu = 2$$, as provided. Would you like a more detailed explanation or have any specific questions? Here are some related questions for you: 1. How do you verify if a probability distribution is valid? 2. What is the difference between expected value and mean in a probability distribution? 3. How would you calculate the variance and standard deviation of this distribution? 4. What would happen if one of the probabilities was negative in this distribution? 5. What are the conditions for a discrete probability distribution? Tip: To check your work, always make sure the sum of the probabilities equals 1.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Probability Distribution
Expected Value (Mean)
Formulas
Mean (μ) = Σ (X * P(X))
Theorems
Sum of probabilities must equal 1
Suitable Grade Level
Grades 9-11
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