CAIE Further Paper 4 2020 Specimen — Question 5

Exam BoardCAIE
ModuleFurther Paper 4 (Further Paper 4)
Year2020
SessionSpecimen
TopicContinuous Probability Distributions and Random Variables
TypeCalculate probability P(X in interval)

5 Th co in rach \& riab e \(X \mathbf { h }\) s prb b lity e \(\mathbf { s }\) ityf \(\mathbf { n }\) tiff \(\dot { \mathrm { g } }\) \& $$f ( x ) = \begin{cases} 0 & x < 0
\frac { 6 } { 5 } x & 0 \leqslant x \leqslant 1
\frac { 6 } { 5 } x ^ { - 4 } & x > 1 \end{cases}$$
  1. FidP \(( X > 1\).
  2. Fid b med arm le \(6 X\).
  3. Gie it \(\mathbf { h } \mathrm { t } \mathrm { E } ( X ) =\), fif id \(\mathbf { b }\) riance \(6 X\).
  4. Fide \(( \sqrt { X } )\).