- The random variable \(W\) has a continuous uniform distribution over the interval \([ - 6 , a ]\) where \(a\) is a constant.
Given that \(\operatorname { Var } ( W ) = 27\)
- show that \(a = 12\)
Given that \(\mathrm { P } ( W > b ) = \frac { 3 } { 5 }\)
- find the value of \(b\)
- find \(\mathrm { P } \left( - 12 < W < \frac { b } { 2 } \right)\)
A piece of wood \(A B\) has length 160 cm . The wood is cut at random into 2 pieces. Each of the pieces is then cut in half. The four pieces are used to form the sides of a rectangle.
- Calculate the probability that the area of the rectangle is greater than \(975 \mathrm {~cm} ^ { 2 }\)