Suppose X Is a Random Variable Whose Probabilities Are Poisson $\mathrm { P } _ { \mathrm { n } }$

question 2

Multiple Choice

Suppose X is a random variable whose probabilities are Poisson distributed with $\mathrm { P } _ { \mathrm { n } }$ = $\frac { ( 14 ) ^ { n } } { n ! }$ $e ^ { - 14 }$ . Which of the following is true?

• A) The probability that x = 14 is approximately 0.1060.
• B) The standard deviation of X is 14.
• C) The expected value of X is \(e ^ { - 14 }\) .
• D) The probability that x = 0 is zero.

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Definitions:

Biodiversity

The variety and variability of life on Earth, including diversity within species, between species, and of ecosystems.

Excessive Ultraviolet Radiation

Overexposure to UV rays from the sun or artificial sources, which can lead to skin damage and increased risk of skin cancer.

Ultraviolet Radiation

A form of energy emitted by the sun, invisible to the naked eye, which can have harmful effects on human skin and eyes but is essential for the synthesis of vitamin D.

Earth

The third planet from the Sun, characterized by its vast oceans, diverse ecosystems, and the presence of life, including human civilization.