normal distribution

Let X, N, Y and Z be random variables. The variables X and N are independent of each other. X is uniformly distributed between -1 and 1; N follows Normal distribution with zero mea...

A random variable X, distributed normally as N(0,1), undergoes the transformation Y = h(X), given in the figure. The form of the probability density function of Y is (In the option...

Let X 1 , X 2 , X 3 and X 4 be independent normal random variables with zero mean and unit variance. The probability that X 4 is the smallest among the four is _______.

Let $$U$$ and $$V$$ be two independent zero mean Gaussian random variables of variances $${1 \over 4}$$ and $${1 \over 9}$$ respectively. The probability $$\,P\left( {3V \ge 2U} \r...

The value of the integral $$1 = {1 \over {\sqrt {2\pi } }}\,\,\int\limits_0^\infty {{e^{ - {\raise0.5ex\hbox{$\scriptstyle {{x^2}}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\sc...

The value of the integral $$\,I = {1 \over {\sqrt {2\,\,\pi } }}\int\limits_0^\infty {\exp \left( { - {{{x^2}} \over 8}} \right)dx} $$ is

A probability density function is given by $$p(x) = \,K\,\,\exp \,\,( - \,{x^2}/2),\,\, - \,\infty \, < \,x < \,\infty $$. The value of K should be