If F(a)=0 then for every x<a, F(x) _______.

P(a<x<b)=_______.

Is function $\mathrm{P}(\mathrm{X}=\mathrm{x})={\left(\frac{1}{ 2 }\right)}^{\mathrm{x}}{\left(\frac{1}{ 2 }\right)}^{1-\mathrm{x}} ; \mathrm{x}=0,1.$ a probabiity function?

$\mathrm{P}(\mathrm{X}=\mathrm{x})=\frac{\mathrm{x}}{ 15 }; \mathrm{x}=1,2,...,5. \mathrm{Then} \mathrm{P}(1 \mathrm{or} 2)=$ _______.

Let $\mathrm{E}\left(\mathrm{x}\right)=5, \mathrm{\sigma }\left(\mathrm{x}\right)=5. \mathrm{Then} \mathrm{E}{(2\mathrm{x}+5)}^2=$ _______.

Three balanced coins are tossed, then mathematical expectation of tails is _______.

A contestant tosses a coin and receives $4 if head appears and pays $3 if tail appears. What is expected value of a trial?

Find c such that $\mathrm{f}\left(\mathrm{x}\right)=\left\{\begin{array}{ll}{\mathrm{cx}}^2 ;& 0<x<3\\ 0 ;& else\end{array}\right.$ is a P.D.F.

For Probability density function $f\left(x\right) = \frac{k}{1+x^2}; -\infty <x<\infty$ , the value of k is _______.

P_ij is called joint probability mass function of (X,Y) provided _______.