TMUA Data Analysis & Statistical Interpretation 5

Question 1

A random variable X has E(X) = 5 and Var(X) = 4. What are E(2X + 3) and Var(2X + 3)?

Accepted Answer

E = 13, Var = 16

Answer

E(2X+3) = 2(5)+3 = 13; Var(2X+3) = 2²×Var(X) = 4×4 = 16.

Question 2

A two-way table shows: P(A) = 0.6, P(B|A) = 0.5, P(B|A') = 0.2. What is P(B)?

Accepted Answer

0.38

Answer

P(B) = P(B|A)P(A) + P(B|A')P(A') = 0.5(0.6)+0.2(0.4) = 0.30+0.08 = 0.38.

Question 3

Data values are 5, 10, 15, 20, 25. Which transformation would most linearise the relationship if the original data appears exponential?

Accepted Answer

Taking the logarithm of each value

Answer

Taking logarithms converts an exponential relationship y = ab^x into a linear one: log y = log a + x log b.

Question 4

A bag contains 4 red and 6 blue balls. Two balls are drawn without replacement. What is the probability that both are red?

Accepted Answer

2/15

Answer

P(both red) = (4/10) × (3/9) = 12/90 = 2/15.

Question 5

A data analyst calculates Spearman's rank correlation coefficient for two variables and obtains rs = −0.85. What does this indicate?

Accepted Answer

A strong negative monotonic relationship

Answer

Spearman's rs near −1 indicates a strong negative monotonic relationship (not necessarily linear).

(TMUA) Test of Mathematics for University Admission Practice Test