Questions & Answers of Random Variables

Weightage of Random Variables

Total 4 Questions have been asked from Random Variables topic of Probability subject in previous GATE papers. Average marks 1.50.

Let X be a Gaussian random variable with mean 0 and variance $\style{font-family:'Times New Roman'}{\sigma^2}$. Let Y= max(X,0) where max(a,b) is the maximum of a and b. The median of Y is ___________.

For any discrete random variable X, with probability mass function

$P(X=j)\;=\;p_j,p_j\geq0,\;\;j\in\{0,......,N\}, $ and $ \sum_{j=0}^N\;p_j=1,\; $ define the polynomial function $ g_X(z)=\overset N{\underset{j=0}{\sum\;}}p_jz^j$. For a certain discrete random variable Y, there exist a scalar $\style{font-family:'Times New Roman'}{\beta\in\left[0,1\right]}$ such that $ g_y(z)=(1-\beta+\beta\;z)^N $. The expectation of Y is 

Four fair six-sided dice are rolled. The probability that the sum of the results being 22 is X1296. The value of X is _________.

Consider a random variable X that takes values +1 and −1 with probability 0.5 each. The values of the cumulative distribution function F(x) at x = −1 and +1 are