Q5 6.1. The point X = (X, Y, Z) is uniformly distributed inside a sphere of radius 1 about the origin. Find the probability of the following events: (a) X is inside a sphere of radius r, r > 0. (b) X is inside a cube of length 2/3 centered about the origin. (c) All components of X are positive. (d) Z is negative.

Q: Please show step by step answer and calculate everything and make the graphic also.

A: a)Proved in explanation sectionb)λ≈5Explanation:a)Given that  Y1​,...,Yn​ are independent Poisson…

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Q: Q5 6.1. The point X = (X, Y, Z) is uniformly distributed inside a sphere of radius 1 about the…

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A: Given fx,y=1x ; 0&lt;y&lt;x&lt;1

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Q: -, P(T|R) P(RT) 9 Consider two events R and T. Find- 1)P(R' UT) = ? = 3 2/7,P( ,P(ROT) = 116 8

A: From the provided information,

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