Statistical and Probabilistic Analysis Flashcards
7 cards from real MS-DS Master of Data science practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Statistical and Probabilistic Analysis flashcards as text
In Bayesian inference, what does the posterior distribution represent?
Answer: Updated belief about a parameter after observing data
The posterior is proportional to the likelihood times the prior, representing updated belief after incorporating observed data.
Which distribution arises as the ratio of a standard normal to the square root of a chi-squared variable divided by its degrees of freedom?
Answer: Student's t-distribution
The t-distribution is defined as Z / √(χ²/ν), where Z is standard normal and χ² has ν degrees of freedom.
A data scientist applies a log transformation to a right-skewed variable before regression. What is the primary statistical reason?
Answer: To reduce skewness and stabilize variance
Log transformation compresses large values, reducing right skew and often stabilizing variance (homoscedasticity).
The moment generating function (MGF) of a random variable X is M(t) = eˢᵗ⁺⁽ˢ²ᵗ²/²⁾. Which distribution does X follow?
Answer: Normal distribution
The MGF of a Normal(μ, σ²) distribution is e^(μt + σ²t²/2), matching the given form with μ=s and σ²=s².
In a one-way ANOVA with 4 groups, what are the degrees of freedom for the between-groups sum of squares?
Answer: 3
Between-groups degrees of freedom = k - 1, where k is the number of groups; for 4 groups, df = 3.
A random sample of size n=36 is drawn from a population with σ=12. What is the standard error of the mean?
Answer: 2
Standard error = σ/√n = 12/√36 = 12/6 = 2.
Which of the following best describes a conjugate prior in Bayesian analysis?
Answer: A prior that yields a posterior in the same distributional family as the prior
Conjugate priors simplify Bayesian computation because the posterior has the same functional form as the prior.