The random variable \(R\) has a continuous uniform distribution over the interval \([ 2,10 ]\)
Write down the probability density function \(\mathrm { f } ( r )\) of \(R\)
A sphere of radius \(R \mathrm {~cm}\) is formed.
The surface area of the sphere, \(S \mathrm {~cm} ^ { 2 }\), is given by \(S = 4 \pi R ^ { 2 }\)
Show that \(\mathrm { E } ( S ) = \frac { 496 \pi } { 3 }\)
The volume of the sphere, \(V \mathrm {~cm} ^ { 3 }\), is given by \(V = \frac { 4 } { 3 } \pi R ^ { 3 }\)
Find, using algebraic integration, the expected value of \(V\)