Math  /  Data & Statistics

Question2. The random variable XX has a distribution with density g(x)={0x<0x8x[0,2)13x24x[2,8)0x>8.g(x)=\left\{\begin{array}{ll} 0 & x<0 \\ \frac{x}{8} & x \in[0,2) \\ \frac{1}{3}-\frac{x}{24} & x \in[2,8) \\ 0 & x>8 \end{array} .\right.
Calculate EX,VarX\mathbb{E} X, \operatorname{Var} X, the skewness coefficient of XX, and the kurtosis of XX.

Studdy Solution
The expected value EX\mathbb{E} X is 6112\frac{61}{12}.
The variance VarX\operatorname{Var} X is 7081144-\frac{7081}{144}.
The skewness and kurtosis require further integration and are conceptually about asymmetry and peakedness.

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