For \(x\in\mathbb{R}\), the floor function is denoted by \(f(x)=\lfloor…

For $x\in\mathbb{R}$, the floor function is denoted by $f(x)=\lfloor x\rfloor$ and defined as follows $\lfloor x\rfloor=k,\ k\leq x<k+1$, where k is an integer. Let $Y=\lfloor X\rfloor$, where X is an exponentially distributed random variable with mean $\frac{1}{\ln10}$, where ln denotes natural logarithm. For any positive integer $\ell$, one can write the probability of the event $Y=\ell$ as follows $P(Y=\ell)=q^\ell(1-q)$. The value of q is