List of top Data Science and Artificial Intelligence Questions on Random variables asked in GATE AR

Two fair coins are tossed independently. X is a random variable that takes a value of 1 if both tosses are heads and 0 otherwise. Y is a random variable that takes a value of 1 if at least one of the tosses is heads and 0 otherwise.
The value of the covariance of X and Y is _________ (rounded off to three decimal places).

Given the following Bayesian Network consisting of four Bernoulli random variables and the associated conditional probability tables :

	P(.)
U = 0	0.5
U = 1	0.5

	P(V = 0| .)	P(V = 1| .)
U = 0	0.5	0.5
U = 1	0.5	0.5
	P(W = 0| .)	P(W = 1| .)
U = 0	1	0
U = 1	0	1

		P(Z = 0| .)	P(Z = 1| .)
V = 0	W = 0	0.5	0.5
V = 0	W = 1	1	0
V = 1	W = 0	1	0
V = 1	W = 1	0.5	0.5

The value of P(U = 1, V = 1, W = 1,Z= 1) = ______. (rounded off to three decimal places)

Given the two-dimensional dataset consisting of 5 data points from two classes (circles and squares) and assume that the Euclidean distance is used to measure the distance between two points. The minimum odd value of k in k-nearest neighbor algorithm for which the diamond (◊) shaped data point is assigned the label square is ________.

Let X be a random variable exponentially distributed with parameter λ > 0. The probability density function of X is given by :
\(f(x) = \left\{ \begin{array}{ll} \lambda e^{-\lambda x,} & x \ge0 \\ 0 & \text{otherwise} \end{array} \right.\)
If 5E(X) = Var (X), where E (X) and Var (X) indicate the expectation and variance of X, respectively, the value of λ is _____
(rounded off to one decimal place).

Let X be a random variable uniformly distributed in the interval [1, 3] and Y be a random variable uniformly distributed in the interval [2, 4]. If X and Y are independent of each other, the probability P(X ≥ Y) is ________
(rounded off three decimal places).

Consider five random variables U, V, W, X, and Y whose joint distribution satisfies :
P(U, V, W, X,Y) = P(U)P(V)P(W|U,V)P(X|W)P(Y|W)
Which ONE of the following statements is FALSE ?