List of top Statistics, Econometrics & Mathematical Economics Questions on Probability asked in GATE XH-C1

For the following function f(x) to be a probability density function, the value of c will be ____________ (rounded off to two decimal places).
\(f(x)=\left\{ \begin{array}{l}\frac{c}{\sqrt{x}};0\lt x\lt 4\ \text{and}\ c\gt0 \\ 0;\ \ \text{otherwise} \end{array} \right.\)

A six-face fair die is rolled once, with X being the number that appeared on the uppermost surface. Then the variance of X is ________ (rounded off to three decimal places).

Two friends Aditi and Raju are deciding independently whether to watch a movie or go to a music concert that evening. Both friends would prefer to spend the evening together than apart. Aditi would prefer that they watch a movie together, while Raju would prefer that they go to the concert together. The payoff matrix arising from their actions is presented below. p and (1 - p) are the probabilities that Aditi will decide in favour of the movie and concert, respectively. Similarly, q and (1 - q) are the probabilities that Raju will decide in favour of the movie and concert, respectively. Which one of the following options correctly contains all the Nash Equilibria ?

		Raju
Aditi		Movie	Concert
	Movie	2,1	0,0
	Concert	0,0	1,2

If X and Y are two random variables with the joint probability density function
\(f(x,y)=\left\{ \begin{array}{l} \frac{2}{3}(x+2y);\ \text{for}\ 0\lt x, y\lt 1 \\ 0;\ \ \ \ \ \ \ \ \ \ \text{otherwise} \end{array} \right.\)
then \(E[X|Y=\frac{1}{2}]\) will be

If a discrete random variable X follows the uniform distribution and assumes only the values 8, 9, 11, 15, 18, and 20, then P(|X -14| < 5) is

Assume the following probabilities for two events, A and B: P(A) = 0.50,P(B) = 0.50, and P(A ∪ B) = 0.85. Then we can conclude that

Let x and y be two dummy variables that take the values of either 0 or 1, and follow the bivariate frequency distribution as given below. If a logit regression is estimated with y as the dependent variable and x as the independent variable, then the estimated coefficient of x is _____ (rounded off to two decimal places)

x	0	1	Total
y
0	6	11	17
1	6	7	13
Total	12	18	30

The estimated results of a Probit model is given in the table below, where Y is a binary variable taking the value either 0 or 1, and X is an integer. The probability that Y = 1 when X = 30 is ________ (rounded off to two decimal places).

Variable	Coefficient	Standard Error	Z-Statistic	Probability
Constant	-0.064	0.399	-0.161	0.871
X	0.029	0.010	2.916	0.003