let x be a random variable with cumulative distribution function `F(x)=x^2, 0ltxlt1` then, `p(1/2ltxlt3/4)=?`

Given the probability density functio (p.d.f) of a continuos random variable X as. f(x)=(x^(2))/(3),-1 lt x lt2 Determine the cumulative distribution function (c.d.f) X and hence find P(X lt1),P(X gt0), P(1 lt X lt 2) .

The pdf of a random variable X is f(x)=3(1-2x^(2)),0ltxlt1 =0" otherwise" The P((1)/(4)ltXlt(1)/(3))= . . .

If X is the a random variable with probability mass function P(x) = kx , for x = 1,2,3 = 0 , otherwise then k = ……..

Let x be a random variable such that the probability function of a distribution is given by P(X=0) =1/2 , P(X = J ) = 1/(3^j) ( j = 1,2,3 ,…..,,oo) then the mean of the distribution and P(X is positive and even) respectively are:

If a random variable X has a poisson distribution such that P(X=1)=P(X=2), its mean and variance are

The mean and variance of the random variable X which follows the following distribution are respectively. X = x:- 1 2 3 4 p( X = x):- 0.1 0.2 0.3 0.4

The variance of the random variable X having the following distribution is {:(X=x:,-2,-1,0,1,2),(P(X=x):,(1)/(6),(1)/(6),(1)/(3),(1)/(6),(1)/(6)):}

The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively.The P(X=1) is