Practice Mean And Variance Using Pdf (13.1.6) - Probability Density Function (pdf)

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9 questions

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6 sample questions

Question 1.
What is the expected value of a continuous random variable with PDF f(x) = 3x² for x from 0 to 1?
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Use the integral definition of expected value.
Question 2.
Define variance.
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Think about variability in data.
3Question 3.
What is the formula for calculating the mean of a continuous random variable?
- E[X] = ∫ f(x) dx
- E[X] = ∫ x f(x) dx
- E[X] = ∫ (x - µ)² f(x) dx
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Focus on what you integrate.
4Question 4.
True or False: Variance can be zero for a random variable.
- True
- False
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Consider what variance measures.
Question 5.
A continuous random variable's PDF is given by f(x) = 12x(1-x) for 0 ≤ x ≤ 1. Calculate the mean and variance.
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Calculate the mean first and then use it to find the variance.
Question 6.
For a normal distribution with mean 5 and standard deviation 2, determine E[X²] and its relationship to the variance.
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Recall the formulas relating mean and variance.

5 more questions in this section. Enroll free to practise them all.