0 for x < α or x > β
20 important questions on 0 for x < α or x > β
How is the expected value \( E(X) \) of a uniform distribution calculated?
- Expected value: \( \frac{\alpha + \beta}{2} \)
- Average of endpoints
What is the formula for variance \( Var(X) \) in a uniform distribution?
- Variance: \( \frac{(\beta - \alpha)^2}{12} \)
- Spread of distribution
How do you calculate the probability \( P(X < 10) \) for \( X \sim U(5, 30) \)?
- Probability calculation:
- - \( \frac{10 - 5}{30 - 5} = \frac{5}{25} = 0.2 \)
- Proportion of interval
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What is the height of the PDF graph for a uniform distribution?
- Height: \( \frac{1}{\beta - \alpha} \)
- Constant value
What represents the endpoints in a uniform distribution?
- Endpoints: \(\alpha, \beta\)
- Start and end of interval
What is needed to calculate P(X < 10) in a uniform distribution?
- Shape: Rectangular
- Formula: area rectangle = base · height
What is the height of the graph in a uniform distribution?
- Calculation: 1 / (30 - 5)
- Result: 1/25
What is the final result for P(X < 10)?
- Conclusion: Calculated area under the graph.
- Valid for uniform distribution.
How is normal distribution represented in notation?
What is the expected value E(X) for a normal distribution?
What is the first step in calculating probabilities?
Which table is used to calculate the probability?
How can we read the table effectively?
What does P(Z < −a) equal?
What does P(Z > −a) equal?
Why do the rules work for standard normal distribution?
How is P(Z < −1.82) rewritten?
How is P(Z > 0.36 rewritten?
What is the calculated value for P(Z > 0.36)?
How is P(Z > −0.75) expressed?
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