Question

Losses \( X \) follow the probability density function \( p d f \) \[ f(x)=\frac{x}{\theta²} e⁻\ᶠʳᵃᶜ{ˣ}{\ᵗʰᵉᵗᵃ}, x>0, \theta>0 . \] \( \rightarrow \) with \( d=\theta \) and imposes a policy lim

A) x
B) θ
C) e
D) d

Answer 1

Continuous probability functions involve the probability density function (pdf) and cumulative distribution function (cdf), where probabilities correspond to areas under the pdf curve. The cdf gives the probability that a variable is less than or equal to a specific value.

Step-by-step explanation:

Understanding Continuous Probability Functions

When dealing with continuous random variables, the probability of an event is represented by the area under the probability density function (pdf) curve. The pdf, denoted as f(x), is always greater than zero and tells us how likely different outcomes are. The entire area under the pdf curve equals one, reflecting the fact that the probability of all possible events sums up to 100%.

The cumulative distribution function (cdf) is another crucial concept in continuous probability. CDF defines the probability that a random variable X is less than or equal to a certain value x, which is expressed as P(X ≤ x). For any two points c and d, the probability that X is between those points is found by calculating the area under the pdf curve from c to d, and is written as P(c < X < d).

In continuous distributions, the probability that X equals any single value is actually zero, because a point has no width and hence no area under the curve. Therefore, when calculating probabilities for continuous random variables, we consider intervals rather than specific values.