Let X Be an Exponential Random Variable With $\lambda$ = 250 Find the Following Probabilities

question 27

Essay

Let X be an exponential random variable with $\lambda$ = 2.50. Find the following probabilities.
a. P(X $\geq$ 1.5).
b. P(X $\leq$ 1).
c. P(0.25 $\leq$ X $\leq$ 0.78).
d. P(X = 0.41).

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Definitions:

Sensation Seeking

The tendency to pursue sensory pleasure and excitement, often involving a higher risk of dangerous activities.

Anti-Social Risk

The potential for an individual to engage in behavior that is harmful or detrimental to society or social norms.

Disinhibition

The reduction of inhibition in behavior, often resulting in actions that are uncharacteristic or forbidden.

Uninhibited Social

Describes a state or behavior where an individual interacts freely and openly without self-consciousness or restraint.