Question

Let X_1, X_2, ... , X_n denote a random sample of size n from a population with a probability density function given by f(x|θ) = exp(-(x-θ)) I_[θ, [infinity])(x). Explain the meaning and significance of this probability density function.

Answer 1

The given probability density function represents the exponential distribution with parameter θ. This distribution is used to describe intervals of time between random events.

Step-by-step explanation:

The given probability density function f(x|θ) = exp(-(x-θ)) I_[θ, [infinity])(x) represents the exponential distribution with parameter θ. This distribution is used when we are interested in the intervals of time between random events. The exponential distribution has a mean of θ and a standard deviation of θ as well. The probability density function f(x) = θe^(-θx) represents the likelihood of observing a specific value of x.