Mathematics, 20.01.2020 19:31 kaylam5599
Let x and y be random variables with the following joint moment generating function: m_{x, y}(s, t)=0.1+0.2e^s+0.3e^t+0.4e^{s+t}
determine pr[x = y].
Answers: 3
![\implies\mathrm{Pr}[X=x,Y=y]=\begin{cases}0.1&\text{for }x=y=0\\0.2&\text{for }x=1,y=0\\0.3&\text{for }x=0,y=1\\0.4&\text{for }x=y=1\\0&\text{otherwise}\end{cases}](/tpl/images/0462/8853/fdcaa.png)
![\mathrm{Pr}[X=Y]=\mathrm{Pr}[X=Y=0]+\mathrm{Pr}[X=Y=1]=0.1+0.4=\boxed{0.5}](/tpl/images/0462/8853/bbf63.png)
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