The radius of a sphere is a random number between 2 and 4. What is the

1.	The radius of a sphere is a random number between 2 and 4. What is the expected value of its volume? What is the probability that its volume is at most 36π? with full explaination..
Answer» Given : The radius of a sphere is a random number between 2 and 4. To Find : What is the EXPECTED value of its VOLUME probability that its volume is at most 36π SOLUTION: Volume of Sphere = (4/3)πR³ The radius of a sphere is a random number between 2 and 4 f(R) = 1/(4- 2) for 2 < R < 4 0 R other value $E(R) = \int\limits^4_2 {\frac{4}{3} \pi R^3 } \, \frac{dR}{2}$ => E (R) = (2π/3) (R⁴/4) $\left \right ]_2^4$ => E (R) = (π/6) [4⁴ - 2⁴] => E (R) = (π/6) [240] => E (R) = 40π expected value of its volume = 40π cubic units 36π = (4/3)πR³ => R = 3 Hence probability that its volume is at most 36π = (3 - 2)/ ( 4- 2) = 1/2 = 0.5 Learn More: A game at the fair INVOLVES a wheel with seven sectors. Two of the ... brainly.in/question/16294455 suppose you remove the jacks, queens and kings from the deck. this ... brainly.in/question/17965282

The radius of a sphere is a random number between 2 and 4. What is the expected value of its volume? What is the probability that its volume is at most 36π? with full explaination..

Answer»

Given : The radius of a sphere is a random number between 2 and 4.

To Find : What is the EXPECTED value of its VOLUME

probability that its volume is at most 36π

Volume of Sphere = (4/3)πR³

The radius of a sphere is a random number between 2 and 4

f(R) = 1/(4- 2) for 2 < R < 4

0 R other value

$E(R) = \int\limits^4_2 {\frac{4}{3} \pi R^3 } \, \frac{dR}{2}$

=> E (R) = (2π/3) (R⁴/4) $\left \right ]_2^4$

=> E (R) = (π/6) [4⁴ - 2⁴]

=> E (R) = (π/6) [240]

=> E (R) = 40π

expected value of its volume = 40π cubic units

36π = (4/3)πR³

=> R = 3

Hence probability that its volume is at most 36π = (3 - 2)/ ( 4- 2)

= 1/2

= 0.5

Learn More:

A game at the fair INVOLVES a wheel with seven sectors. Two of the ...

suppose you remove the jacks, queens and kings from the deck. this ...