MS-DS Master of Data science Statistical and Probabilistic Analysis 2

Question 1

A dataset has a mean of 50 and a standard deviation of 10. Using Chebyshev's inequality, what is the minimum proportion of data within 3 standard deviations of the mean?

Accepted Answer

At least 88.9%

Answer

Chebyshev's inequality states at least 1 - 1/k² of data lies within k standard deviations; for k=3, that's 1 - 1/9 ≈ 88.9%.

Question 2

Which test is most appropriate to assess whether two continuous variables are linearly associated when both are normally distributed?

Accepted Answer

Pearson correlation test

Answer

Pearson correlation tests linear association between two normally distributed continuous variables and is parametric.

Question 3

In a Type II error scenario, a researcher fails to reject a null hypothesis that is actually false. Which factor, if increased, most directly reduces this error?

Accepted Answer

Sample size

Answer

Increasing sample size reduces the standard error, increasing statistical power and reducing the probability of a Type II error (β).

Question 4

A random variable X follows a Poisson distribution with λ = 4. What is P(X = 0)?

Accepted Answer

e⁻⁴

Answer

For Poisson, P(X=k) = (λᵏ e⁻λ)/k!; at k=0, this simplifies to e⁻⁴.

Question 5

The joint probability P(A ∩ B) = 0.12, P(A) = 0.4, and P(B) = 0.3. Are events A and B independent?

Accepted Answer

Yes, because P(A)·P(B) = 0.12

Answer

Independence holds when P(A ∩ B) = P(A)·P(B); here 0.4 × 0.3 = 0.12, which matches.

MS-DS Master of Data science Practice Test

MS-DS Master of Data science Practice Test

MS-DS Master of Data science Statistical and Probabilistic Analysis 2