Question

An actuary analyzes a company's annual personal auto claims, m, and annual commercial auto claims, n. the analysis reveals that var(m) = 1600, var(n) = 900, and the correlation between m and n is 0.64. calculate var(m + n). (a) 768 (b) 2500 (c) 3268 (d) 4036 (e) 4420

Answer 1

D

Explanation:

Since 2 variables are inter-dependent (there is correlation between them given as 0.64), we need to use the formula shown below:

Var(x+y) = Var(x) + Var(y) + 2 * correlation coefficient *
`√(Var(x))` *
`√(Var(y))`

Given Var(m) = 1600, Var(n) = 900 and correlation coefficient 0.64, we plug them into the formula and solve:

Var (m+n) = Var(m) + Var(n) + 2 * correlation coefficient *
`√(Var(m))` *
`√(Var(n))`

= 1600 + 900 + 2(0.64)*Sqrt(1600)*Sqrt(900)

= 4036

correct answer d