Consider a random variable with exponential distribution with y=1 .compute the probability for P(x>2)
To compute the probability P(x > 2) for a random variable with exponential distribution with parameter λ=1, we can use the cumulative distribution function (CDF) of the exponential distribution.
The CDF of an exponential distribution with parameter λ is given as:
F(x) = 1 - e^(-λx)
In this case, λ = 1, so the CDF becomes:
F(x) = 1 - e^(-x)
To calculate P(x > 2), we need to subtract the cumulative probability up to x = 2 from 1. So, we have:
P(x > 2) = 1 - F(2)
= 1 - (1 - e^(-2))
= e^(-2)
Therefore, P(x > 2) is equal to e^(-2) which is approximately 0.13534.