The amount of snowfall in feet in a remote region of Alaska in the month of January is a continuous random variable with probability density function Find the amount of snowfall one can expect in any given month of January in Alaska.
A) 7.5 ft
B) 4 ft
C) 2.5 ft
D) 3.5 ft

Question

The amount of snowfall in feet in a remote region of Alaska in the month of January is a continuous random variable with probability density function  Find the amount of snowfall one can expect in any given month of January in Alaska.
A) 7.5 ft 
B) 4 ft 
C) 2.5 ft 
D) 3.5 ft

Quizplus · Accepted Answer

To find the expected amount of snowfall, we need to calculate the mean of the probability density function. Integration of the given PDF from 0 to infinity gives us the value of 1. So, we need to evaluate the integral from 0 to infinity of xf(x) dx, where f(x) is the PDF given.

Evaluating this integral, we get the expected value of snowfall as:

E(X) = ∫0∞ x(11e^(-x/4)) dx = 4(11) = 44

Therefore, the expected amount of snowfall in any given month of January in Alaska is 44/12 = 3.67 ft. Since none of the answer choices exactly match this value, the closest choice is D) 3.5 ft.

The Amount of Snowfall in Feet in a Remote Region