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quiz Informatik · 10 questions

Fundamentals of Statistical Learning

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1

If two events A and B are independent, which of the following equalities must hold?

2

Given a discrete random variable X with pmf f_X(x), which expression correctly relates its CDF to the pmf?

3

In a Bernoulli experiment with unknown success probability θ, the method-of-moments estimator for θ is:

4

For a random vector X = (X1,…,Xk)ᵀ, which statement correctly describes the marginal pdf of Xi when the joint pdf is f_X(x)?

5

Which of the following is the variance decomposition known as the law of total variance?

6

A test statistic T_n = Σ_{j=1}^k (N_j - n p_{0j})^2 / (n p_{0j}) converges in distribution to which of the following under H0?

7

In linear regression, assuming XᵀX is invertible, the least squares estimator β̂ satisfies which equation?

8

For a random variable X with finite mean μ and variance σ², Chebyshev’s inequality provides a bound for P(|X-μ| ≥ t). Which of the following is that bound?

9

When testing H₀: θ = θ₀ versus H₁: θ ≠ θ₀ with an asymptotically normal estimator θ̂, the Wald test rejects H₀ if:

10

In logistic regression, the log‑likelihood gradient can be expressed as Xᵀ (Y - μ(β)). What does μ_i(β) represent?

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