List of top Statistics Questions asked in GATE XH-C1

Suppose from the estimation of a linear regression model \(Y_i=\beta_0+\beta_1X_i+e_i\) the residual sum of squares and the total sum of squares are obtained as 44 and 80, respectively. The value of coefficient of determination is ____________ (round off to two decimal places).

Let $X$ be a random variable with pdf $f(x)=\dfrac{1}{2\sqrt{3}}$ for $-\sqrt{3}<x<\sqrt{3}$, and $0$ otherwise. Then, the variance of $X$ is _____(in integer)}.

The following table provides population information for different age groups in 2010 and 2017. The percentage change in old-age dependency ratio from 2010 to 2017 is ____________ (round off to two decimal places).

Age group	Population in 2010	Population in 2017
0 to 14 years	201630	213609
15 to 64 years	899210	847552
65 years and above	232450	254474

Which of the following is/are used for testing the assumption of normality?

Consider a lottery with two possible outcomes:

Rupees 100 with probability 0.6
Rupees 50 with probability 0.4 The maximum amount that a risk-neutral person would be willing to pay to play the above lottery equals Rupees _________ (in integer).

Mr. Sharma’s consumption preference for tea (denoted by \( x \)) and sugar (denoted by \( y \)) is given by the utility function \[ U(x,y) = \min(x, 2y) \] The price per unit of tea is 10 and the price per unit of sugar is 10. Mr. Sharma’s total income is 900. The optimum quantity of tea purchased by Mr. Sharma equals _________ (in integer).

Which one of the following is a test of heteroscedasticity?

An economy is characterized by the following production function: \[ Y = A K^{0.25} L^{0.75} \] where \(K\) denotes capital, \(L\) denotes labour, \(A\) denotes the total factor productivity, and \(Y\) denotes output produced. All capital and labour are fully employed. Suppose that the growth rate of labour is 1%, the growth rate of capital is 4%, and the growth rate of output is 4%. The growth rate of total factor productivity \(A\) is: