The moment generating functions of three independent random variables X, Y and Z are respectively given as MX(t) = 1/9 (2 + e^t)^2, ; t in R, MY(t) = e^(e^t - 1), ; t in R, and MZ(t) = e^2(e^t - 1), ; t in R. Then 10 Pr(X Y + Z) equals (rounded off to two decimal places).

Q58Section ST (Statistics (Q11–Q65))58 of 65

P(X > Y+Z) from mgfs

The moment generating functions of three independent random variables $X$ , $Y$ and $Z$ are respectively given as $M_X(t) = \frac{1}{9} (2 + e^t)^2, \; t \in \mathbb{R}$ , $M_Y(t) = e^{(e^t - 1)}, \; t \in \mathbb{R}$ , and $M_Z(t) = e^{2(e^t - 1)}, \; t \in \mathbb{R}$ . Then $10 \operatorname{Pr}(X > Y + Z)$ equals __________ (rounded off to two decimal places).

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