probability density function

The graph of a function f(x) is shown in the figure. For f(x) to be a valid probability density function, the value of h is

For the function f(x)=a+bx, 0 ≤ x ≤ 1, to be a valid probability density function, which one of the following statements is correct?

For the function $$\,f\left( x \right) = a + bx,0 \le x \le 1,\,\,$$ to be a valid probability density function, which one of the following statements is correct?

If $$f(x)$$ and $$g(x)$$ are two probability density functions, $$$f\left( x \right) = \left\{ {\matrix{ {{x \over a} + 1} & : & { - a \le x < 0} \cr { - {x \over a} + 1} & : & {0...

The probability density function of a random variable, $$x$$ is $$$\matrix{ {f\left( x \right) = {x \over 4}\left( {4 - {x^2}} \right)} & {for\,\,0 \le x \le 2 = 0} \cr { = 0} & {o...

If $$\left\{ x \right\}$$ is a continuous, real valued random variable defined over the interval $$\left( { - \infty ,\,\, \pm \infty } \right)$$ and its occurrence is defined by t...

The probability density function of evaporation $$E$$ on any day during a year in a watershed is given by $$$f\left( E \right) = \left\{ {\matrix{ {{1 \over 5}} & {0 \le E \le 5\,m...

Find the value of $$\lambda $$ such that the function $$f(x)$$ is a valid probability density function ________.