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 the density function given as: $$f\left( x \right) = {1 \over {\sqrt {2\pi * b} }}{e^{ - {1 \over 2}{{\left( {{{x - a} \over b}} \right)}^2}}}$$ where $$'a'$$ and $$'b'$$ are the statistical attributes of the random variable $$\left\{ x \right\}$$. The value of the integral $$\int\limits_{ - \infty }^a {{1 \over {\sqrt {2\pi * b} }}{e^{ - {1 \over 2}{{\left( {{{x - a} \over b}} \right)}^2}}}} dx\,\,\,$$ is

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

Is an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most one negative value in five trials is

There are two containers with one containing $$4$$ red and $$3$$ green balls and the other containing $$3$$ blue balls and $$4$$ green balls. One ball is drawn at random from each container. The probability that one of the balls is red and the other is blue will be ___________.