List of top Engineering Mathematics Questions on Probability and Statistics

If X is a Poisson random variable with variance \(P(X = 2) = 9 P(X = 4)\) then the mean and variance respectively are
If X and Y are independent random variables with variances \(\sigma_x^2 = 5\) and \(\sigma_y^2 = 3\) then the variance of the random variable \(Z = 3X + 2Y - 5\) is
Bag-I contains 4 white and 6 black balls, Bag-II contains 4 white and 3 black balls. A ball is selected at random and it comes out to be a black ball. What is the probability that it is from Bag-I?
Two fair dice are rolled, and the random variable \( X \) denotes the sum of the outcomes. What is the expected value of \( X \)?

Which of the following probability distribution functions (PDFs) has the mean greater than the median?