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

question 110

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:

Total Metabolic Rate

The total amount of energy expended by an organism in a given time period to maintain all bodily functions while at rest.

Basal Metabolic Rate

The rate at which the body uses energy while at rest to maintain vital functions such as breathing and keeping warm.

Body Mass Index

A measure of body fat based on height and weight that applies to adult men and women, used to classify underweight, normal weight, overweight, and obesity.

Metabolic Rate

Metabolic Rate is the rate at which an organism's body consumes energy, crucial for determining the amount of food energy it needs to maintain its body functions.