91Ó°ÊÓ

The random variable X follows the uniform distribution on the interval [-2,8].

The probability density function of a continuous uniform distribution over the support [a,b] is given as,

\(f\left( x \right) = \left\{ \begin{array}{l}\frac{1}{{b - a}}\;\;\;\;\;\;\;for\;a \le x \le b\\0\;\;\;\;\;\;\;\;\;\;\;\;\;otherwise\end{array} \right.\)

Since X follows the uniform distribution with \(a = - 2\) and \(b = 8\), the probability density function is,

\(\begin{aligned}{}f\left( x \right)& = \frac{1}{{8 - \left( { - 2} \right)}}\\ &= \frac{1}{{10}}\end{aligned}\)

The probability that X falls between 0 and 7 is computed as,

\(\begin{aligned}{}P\left( {0 < X < 7} \right) &= \int\limits_0^7 {\frac{1}{{10}}dx} \\ &= \left( {\frac{x}{{10}}} \right)_0^7\\ &= \frac{7}{{10}}\\& = 0.7\end{aligned}\)

Therefore, the required probability of X is 0.7.