Practice Marginal Pdf (continuous) (14.3.2) - Joint Probability Distributions

Practice: Marginal PDF (Continuous)

Lesson 14.3.2Joint Probability Distributions

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9 questions

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Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the marginal PDF of X if the joint PDF is f(x,y) = 6xy for 0 ≤ x, y ≤ 1?
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Integrate 6xy with respect to y from 0 to 1.
Question 2.
State the condition for marginal PDFs in relation to joint PDFs.
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Consider the definition of probability density functions.
3Question 3.
What does the marginal PDF represent?
- The probability distribution of multiple variables
- The distribution of a single variable from a joint distribution
- The cumulative distribution function
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Think about the term 'marginal' and its meaning in statistics.
4Question 4.
Integration is used to find marginal PDFs because it allows for:
- True
- False
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Recall the purpose of integration in mathematics.
Question 5.
Given the joint probability density function f(x,y) = 3x^2y for 0<x<1 and 0<y<1, derive f_X(x) and f_Y(y).
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Check your limits and ensure proper integration across defined boundaries.
Question 6.
A researcher calculates the marginal PDF of X as f_X(x)=x^2 for x≥0. If the joint PDF integrates to 1, what does it indicate about Y?
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Remember that joint distributions always require summation to 1 across all dimensions.

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