Master random variables and probability distributions with 10 comprehensive questions covering discrete and continuous distributions, joint distributions, and sampling distributions.
10
Total Questions
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Correct Answers
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Questions Attempted
Random Variable Properties
1 questions
Question 1: Distribution Function Continuity
Which statement about random variables is correct?...
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Discrete Distributions
1 questions
Question 2: Binomial Distribution Calculation
Let X ~ B(5, 0.2) (binomial distribution). What is P(X = 2)?...
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Continuous Distributions
1 questions
Question 3: Normal Distribution Standardization
If X ~ N(2, 4) (normal distribution), then Y = (X-2)/2 follows which distribution?...
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Distribution Properties
1 questions
Question 4: Memoryless Property
Which distribution has the 'memoryless property'?...
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Joint Distributions
1 questions
Question 5: Independence Test
For discrete random vector (X,Y) with joint PMF shown in the table below, are X and Y independent? X...
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Distribution Addition
1 questions
Question 6: Poisson Distribution Additivity
If X ~ P(3) and Y ~ P(2), and X and Y are independent, then X+Y follows which distribution?...
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Uniform Distribution
1 questions
Question 7: Uniform Probability Calculation
If X ~ U(1,5) (uniform distribution), what is P(2 < X < 4)?...
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Chi-squared Distribution
1 questions
Question 8: Chi-squared Additivity
If X ~ χ²(4) and Y ~ χ²(6), and X and Y are independent, then X+Y follows which distribution?...
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Probability Density Functions
1 questions
Question 9: PDF Normalization
For a continuous random variable X with PDF p(x) = kx for 0 < x < 2 and 0 otherwise, what is the val...
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Sampling Distributions
1 questions
Question 10: t-Distribution Relationship
If X ~ t(5) (t-distribution with 5 degrees of freedom), then X² follows which distribution?...
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