Find $$$P{\left(X = 3 \right)}$$$ for exponential distribution with $$$\lambda = 0.5$$$

Calculate the various values for the exponential distribution with $$$\lambda = 0.5 = \frac{1}{2}$$$ and $$$x = 3$$$.

Mean: $$$\mu = \frac{1}{\lambda} = 2$$$A.

Variance: $$$\sigma^{2} = \frac{1}{\lambda^{2}} = 4$$$A.

Standard deviation: $$$\sigma = \sqrt{\frac{1}{\lambda^{2}}} = 2$$$A.

$$$P{\left(X = 3 \right)} = 0$$$A

$$$P{\left(X \lt 3 \right)}\approx 0.77686983985157$$$A

$$$P{\left(X \leq 3 \right)}\approx 0.77686983985157$$$A

$$$P{\left(X \gt 3 \right)}\approx 0.22313016014843$$$A

$$$P{\left(X \geq 3 \right)}\approx 0.22313016014843$$$A