Digital Characteristics & Characteristic Functions Practice
Master digital characteristics through 10 comprehensive questions covering expectation, variance, covariance, moments, and characteristic functions with detailed explanations.
10
Total Questions
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Correct Answers
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Questions Attempted
Mathematical Expectation
2 questions
Question 1: Second Moment of Poisson Distribution
Let ξ ~ P(λ) (Poisson distribution). What is the value of E[ξ²]?...
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Question 4: Uniform Distribution Expectation
Let ξ ~ U[1,3] (uniform distribution). What is the value of E(2ξ + 5)?...
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Variance Properties
1 questions
Question 2: Linear Combination Variance
Let ξ and η be independent with E[ξ] = 2, Var(ξ) = 1, E[η] = 3, Var(η) = 2. What is Var(2ξ - η + 1)?...
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Correlation Coefficient
1 questions
Question 3: Properties of Correlation Coefficient
Which statement about correlation coefficient r_{ξη} is INCORRECT?...
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Characteristic Functions
2 questions
Question 5: Normal Distribution Identification
A random variable has characteristic function f(t) = e^{2it - (3/2)t²}. What distribution does it fo...
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Question 10: Symmetric Distribution Identification
A random variable has characteristic function f(t) = cos(t). What is its distribution?...
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Covariance
1 questions
Question 6: Independence and Covariance
Let ξ and η be uncorrelated with E[ξ] = 0, E[η] = 0. What is the value of E(ξη)?...
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Exponential Distribution
1 questions
Question 7: Third Moment of Exponential Distribution
Let ξ ~ Exp(λ) (exponential distribution). What is the value of E[ξ³]?...
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Chebyshev Inequality
1 questions
Question 8: Probability Bound Estimation
Using Chebyshev's inequality to estimate P(|ξ - E[ξ]| ≥ 3√Var(ξ)), the upper bound is:...
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Multivariate Normal
1 questions
Question 9: Bivariate Normal Independence
Let (ξ,η) ~ N(a,b,σ₁²,σ₂²,0) (bivariate normal distribution). What is the relationship between ξ and...
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