continuous-random-variable

Consider a probability distribution given by the density function $P(x)$. $$P(x)=\left\{\begin{array}{cc} C x^2, & \text { for } 1 \leq x \leq 4 \\ 0, & \text { for } x 4 \end{arra...

The unit interval $(0,1)$ is divided at a point chosen uniformly distributed over $(0,1)$ in $R$ into two disjoint subintervals. The expected length of the subinterval that contain...

Suppose you break a stick of unit length at a point chosen uniformaly at random. Then the expected length of the shorter stick is __________________.

Let $$f(x)$$ be the continuous probability density function of a random variable X. The probability that $$a\, < \,X\, \le \,b$$, is: