random variables

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...

Suppose X and Y are independent and identically distributed random variables that are distributed uniformly in the interval [0,1]. The probability that X≥Y is _________.

Two continuous random variables X and Y are related as Y = 2X + 3. Let $$\sigma _x^2$$ and $$\sigma _y^2$$ denote the variances of X and Y, respectively. The variances are related...

If X and Y are random variables such that E[2X + Y] = 0 and E[X + 2Y] = 33, then E[X] + E[Y] = _________.

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

Consider two identically distributed zero - mean random variables $$U$$ and $$V.$$ Let the cumulative distribution functions of $$U$$ and $$2V$$ be $$F(x)$$ and $$G(x)$$ respective...