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Q17Section A (Section A)17 of 60

Uniform MGF and two probes

Let XX be a continuous random variable having the moment generating function M(t)=et−1t,t≠0.M(t)=\frac{e^{t}-1}{t},\quad t\neq 0. Let α=P(48X2−40X+3>0)\alpha=P(48X^{2}-40X+3>0) and β=P((ln⁡X)2+2ln⁡X−3>0)\beta=P\left((\ln X)^{2}+2\ln X-3>0\right). Then, the value of α−2ln⁡β\alpha-2\ln\beta is equal to

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