The random variable $$$X$$$ has probability density function f given by $$\[ \mathrm{f}(x)= \begin{cases}\frac{1}{21}(x-1)^{2} & 2 \leqslant x \leqslant 5 \\ 0 & \text { otherwise }\end{cases} \]$$ Find $$$\mathrm{E}(Y)$$$. ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ .

Further Mathematics

IGCSE&ALevel

CAIE

Exam No：9231_w24_qp_42 Year：2024 Question No：4(d)

Answer:

4.1.2 use the general result where f(x) is the probability density function of the continuous random variable X and g(X) is a function of X