List of top Statistics for Economics Questions asked in IIT JAM

Let 𝑦̂=5.5+3.2 π‘₯ be an estimated regression equation using a large sample. The 95% confidence interval of the coefficient of π‘₯ is [0.26, 6.14] and 𝑅2 = 0.26. The standard error of the estimated coefficient is _______ (round off to 1 decimal place).
Let πœ‹ be the proportion of a population vaccinated against a disease. An estimate Μ‚πœ‹ = 0.64 is found using a sample of 100 individuals from the population. The 𝑧 test statistic for the null hypothesis 𝐻0 : πœ‹ = 0.58 is ________ (round off to 2 decimal places).
Let π‘Œ ∼ π‘π‘œπ‘Ÿπ‘šπ‘Žπ‘™(3, 1), π‘Š ∼ π‘π‘œπ‘Ÿπ‘šπ‘Žπ‘™(1, 2) and 𝑋 ∼ π΅π‘’π‘Ÿπ‘›π‘œπ‘’π‘™π‘™π‘– (𝑝 = 0.9) where 𝑋 = 1 is success and 𝑋 = 0 is failure. Let 𝑆 = π‘‹π‘Œ + (1 βˆ’ 𝑋)π‘Š. Then 𝐸(𝑆) = _________ (round off to 1 decimal place)
If 𝑋 denotes the sum of the numbers appearing on a throw of two fair six-faced dice then the probability
𝑃( 7 < 𝑋 < 10) = ______ (round off to 2 decimal places).
The portfolio of an investment firm comprises of two risky assets, 𝑆 and 𝑇, whose returns are denoted by random variables 𝑅𝑠 and 𝑅𝑇 respectively. The mean, the variance and the covariance of the returns are
𝐸(𝑅𝑠 ) = 0.08, π‘‰π‘Žπ‘Ÿ(𝑅𝑠 ) = 0.07, 
𝐸(𝑅𝑇 ) = 0.05, π‘‰π‘Žπ‘Ÿ(𝑅𝑇 ) = 0.05, πΆπ‘œπ‘£(𝑅𝑠 , 𝑅𝑇 ) = 0.04. 
Let 𝑀 be the proportion of assets allotted to 𝑆 so that the return from the portfolio is 𝑅 = 𝑀𝑅𝑠 + (1 βˆ’ 𝑀)𝑅𝑇 . The value of 𝑀 which minimizes π‘‰π‘Žπ‘Ÿ(𝑅) is _____(round off to 2 decimal places)
A number π‘₯ is randomly chosen from the set of the first 100 natural numbers. The probability that π‘₯ satisfies the condition \(π‘₯ + \frac{300}{π‘₯} > 65\) is ______ (round off to 2 decimal places).