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12.4 Exercise 19

Avg difficulty 2.5

(See Exercise 9 from "Problems on Mathematical Expectation"). Random variable X has density function

f X ( t ) = ( 6 / 5 ) t 2 for 0 ≤ t ≤ 1 ( 6 / 5 ) ( 2 - t ) for 1 < t ≤ 2 = I [ 0 , 1 ] ( t ) 6 5 t 2 + I ( 1 , 2 ] ( t ) 6 5 ( 2 - t ) f_{X} \left(t\right) = \left\{\begin{matrix} \left(6 / 5\right) t^{2} & \text{for} 0 \leq t \leq 1 \\ \left(6 / 5\right) \left(2 - t\right) & \text{for} 1 < t \leq 2 \end{matrix}\right = I \left[0 , 1\right] \left(t\right) \frac{6}{5} t^{2} + I_{\left(1 , 2\right]} \left(t\right) \frac{6}{5} \left(2 - t\right)

E[X]=11/10E \left[X\right] = 11 / 10. Determine Var [X]Var \left[X\right].

Pfeiffer, Applied Probability, 12.4 Problems on Variance, Covariance, Linear Regression, exercise 19

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Adapted from Applied Probability © 2009 Paul E. Pfeiffer. Licensed under CC BY 3.0. Source: Applied Probability. Imported at revision d7a0420.