Question

A random variable X has probability distribution function

f(x) = A + Bx, O ≤ x ≤ 1, If E(X) = $\frac { 1 } { 2 }$ , then (A, B)

• A. (1, 0)
• B. (0, 1)
• C. (1/2, ½)
• D. (1, 1)

Answer 1

Answer: (A)

(1, 0)

Answer 2

2A + B = 2

$\int _ { 0 } ^ { 1 } \mathrm { xf } ( \mathrm { x } ) \mathrm { dx } = \frac { 1 } { 2 } ; \int _ { 0 } ^ { 1 } \left( \mathrm { Ax } + \mathrm { Bx } ^ { 2 } \right) \mathrm { dx } = \frac { 1 } { 2 }$

$\frac { \mathrm { A } } { 2 } + \frac { \mathrm { B } } { 3 } = \frac { 1 } { 2 }$

Solving A=1, B=0