List of top Data Science and Artificial Intelligence Questions on Probability and Statistics

Let L = lim$_{n \to \infty \sum_{k=0}^{n} \frac{e^{-n} }n^k}{k!}$ value of L

Let X be a random variable that follows uniform (-1, 1) dist. The conditional dist. of the random variable Y given X = x is the Uniform (x$^2$ - 0.1, x$^2$ + 0.1) dist. The value of correlation (X, Y) is _______.

A$_{5\times5$ each element following Bernoulli (P = 0.50) Dist. independently. The prob. that row sum of the second row and column sum of the third column are both equal to 3 is-}

Let X be a discrete valued random variable with cumulative dist. F(x) is/are correct:

A clinic specializes in testing for a Disease D. The result of the test can be either positive (+ve) or negative (-ve). A study reveals that if a person suffers from the Disease D, the test result in that clinic comes up +ve 80% of the time and negative 20% of the time. If a person is not suffering from the Disease D, the test comes out positive 10% of the time \& negative 90% of the time. It is also known among the general population the disease D occurs in 30% of the individuals. If the person tests positive for D in that clinic, the probability that he/she actually suffers from the Disease D is __________ (Round off to 2 decimal places).