5. Suppose that a point (X, Y, Z) is to be chosen at random in three-dimensional space, where X, Y, and Z are independent random variables and each has the standard normal distribution. What is the probability that the distance from the (0,0,0) to the point will be less than 1?

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5. Suppose that a point (X, Y, Z) is to be chosen at random in three-dimensional space,
where X, Y, and Z are independent random variables and each has the standard normal
distribution. What is the probability that the distance from the (0,0,0) to the point will
be less than 1?
Transcribed Image Text:5. Suppose that a point (X, Y, Z) is to be chosen at random in three-dimensional space, where X, Y, and Z are independent random variables and each has the standard normal distribution. What is the probability that the distance from the (0,0,0) to the point will be less than 1?
Expert Solution
Step 1: Given information.

Given that:

open parentheses X comma Y comma Z close parentheses is a point chosen in three-dimensional space.
X comma space Y comma space and space Z are three independent standard normal random variables.

To find:

The probability that the distance from the (0,0,0) to the point will be less than 1.

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