List of top Statistics for Economics Questions

Let the value of a random sample drawn from a normal distribution with mean 5 and unknown standard deviation $\sigma$ be 4.8, 4.5, 5.1, 5.2, 5.3, 5.5. Then, the maximum likelihood estimate of $\sigma^2$ is _____. (rounded off to two decimal places).

A regression equation 𝑌 = −2.5 + 2𝑋 is estimated using the following data:

𝑌	2	5	9	14
𝑋	2	4	6	8

The coefficient of determination is ________ (rounded off to two decimal places).

There are 32 students in a class. Three courses namely English, Hindi and Mathematics are offered to them. Each student must register for at least one course. If 16 students take English, 8 students take Hindi, 18 students take Mathematics, 4 students take both English and Hindi, 5 students take both Hindi and Mathematics, and 5 students take both English and Mathematics, then the number of students who take Mathematics only is (in integer).

Two students 𝐴 and 𝐵 are assigned to solve a problem separately. The (conditional) probability that 𝐴 can solve the problem given that 𝐵 cannot solve it, is 1/5. The (conditional) probability that 𝐵 can solve the problem given that 𝐴 can solve the problem is 3/5 . The probability that 𝐴 can solve the problem is 1/10.Then, the probability that 𝐵 can solve the problem is ______ (rounded off to one decimal place).

Let $X_1, X_2, … , X_𝑛$ be a random sample of size n > 1 drawn from a probability distribution having mean $\mu$ and non-zero variance $\sigma^2$. Then, which of the following is/are CORRECT?

Let a random variable X has mean $\mu_x$ and non-zero variance $ \sigma ^2 _x$, and another X random variable Y has mean $\mu_y$ and non zero variance $\sigma ^2 _y$. If the correlation Y coefficient between X and Y is $\rho$, then which of the following is/are CORRECT?

Consider two independent random variables: $X ∼ N(5, 4)$ and $Y~N(3, 2)$. If $(2X + 3Y)~N(\mu, \sigma ^2)$, then the values of mean ($\mu$) and variance ($\sigma ^2$) are

Two distinct integers are chosen randomly from 5 consecutive integers. If the random variable x represents the absolute difference between them, then the mean and variance of x are, respectively,

Suppose a random variable 𝑋 follows an exponential distribution with mean 50. Then, the value of the conditional probability $ P(X > 70 | X > 60)$ is

Let 𝑥 and 𝑦 be two consumption bundles, assumed to be non-negative and perfectly divisible. Further, the assumptions of completeness, transitivity, reflexivity, non-satiation, continuity, and strict convexity are satisfied. Then, which of the following statements is NOT CORRECT?

Which one of the following is a non-parametric test?

Consider an Economy that produces only Apples and Bananas. The following Table contains per unit price (in INR) and quantity (in kg) of these goods. Assuming 2010 as the Base Year and using GDP deflator to calculate the annual inflation rate, which of the following options is CORRECT?

Year	Price of Apple	Quantity of Apple	Price of Banana	Quantity of Banana
2010	1	100	2	50
2011	1	200	2	100
2012	2	200	4	100

Let 𝑀 and 𝑁 be events defined on the sample space 𝑆. If 𝑃(𝑀) = \(\frac{1}{3}\) and 𝑃(𝑁^𝑐 ) = \(\frac{1}{4}\) then which one of the following is necessarily CORRECT?

Which of the following functions qualify to be a cumulative density function of a random variable 𝑋 ?

Let the joint probability density function of the random variables 𝑋 and 𝑌 be
\(f(x,y) =   \begin{cases} 1,     & \quad 0<x<1,\,\,\,\,x<y<x+1\\   0,& \quad \ \text{ Otherwise}   \end{cases}\)
Let the marginal density of 𝑋 and 𝑌 be 𝑓_𝑋(𝑥) and 𝑓_𝑌 (𝑦), respectively. Which of the following is/are CORRECT?

Let X∼Normal (0, 1) and 𝑌 = |𝑋|. If the probability density function of 𝑌 is 𝑓𝑌 (y) then for 𝑦>0,\( \sqrt{\frac{\pi}{2}}\) 𝑓𝑌 (𝑦) is

Let 𝑋 ∼ 𝑈𝑛𝑖𝑓𝑜𝑟𝑚 8, 20) and 𝑍 ∼ 𝑈𝑛𝑖𝑓𝑜𝑟𝑚(0, 6) be independent random variables. Let 𝑌 = 𝑋 + 𝑍 and 𝑊 = 𝑋 − 𝑍. Then 𝐶𝑜𝑣(𝑌, 𝑊) is ______ (in integer).

Let the probability density function of the continuous random variable 𝑋 be
, 0, 𝑥 ≥ 0 otherwise , 
where 𝜆 > 0 is a parameter. If the observed sample values of 𝑋 are 
𝑥₁ = 1.75, 𝑥₂ = 2.25, 𝑥₃ = 2.50, 𝑥4 = 2.75, 𝑥₅ = 3.25, then the Maximum Likelihood Estimator of 𝜆 is

Let 𝑌 ∼ 𝑁𝑜𝑟𝑚𝑎𝑙(3, 1), 𝑊 ∼ 𝑁𝑜𝑟𝑚𝑎𝑙(1, 2) and 𝑋 ∼ 𝐵𝑒𝑟𝑛𝑜𝑢𝑙𝑙𝑖 (𝑝 = 0.9) where 𝑋 = 1 is success and 𝑋 = 0 is failure. Let 𝑆 = 𝑋𝑌 + (1 − 𝑋)𝑊. Then 𝐸(𝑆) = _________ (round off to 1 decimal place)

From a set comprising of 10 students, four girls 𝐺_𝑖 , 𝑖 = 1, … , 4, and six boys 𝐵_𝑗 , 𝑗 = 1, … , 6, a team of five students is to be formed. The probability that a randomly selected team comprises of 2 girls and 3 boys, with at least one of them to be 𝐵₁ or 𝐵₂ , is equal to

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).

Let 𝑦̂=5.5+3.2 𝑥 be an estimated regression equation using a large sample. The 95% confidence interval of the coefficient of 𝑥 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 be the proportion of a population vaccinated against a disease. An estimate ̂𝜋 = 0.64 is found using a sample of 100 individuals from the population. The 𝑧 test statistic for the null hypothesis 𝐻₀ : 𝜋 = 0.58 is ________ (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 𝑅_𝑠 and 𝑅_𝑇 respectively. The mean, the variance and the covariance of the returns are
𝐸(𝑅_𝑠 ) = 0.08, 𝑉𝑎𝑟(𝑅_𝑠 ) = 0.07, 
𝐸(𝑅_𝑇 ) = 0.05, 𝑉𝑎𝑟(𝑅_𝑇 ) = 0.05, 𝐶𝑜𝑣(𝑅𝑠 , 𝑅_𝑇 ) = 0.04. 
Let 𝑤 be the proportion of assets allotted to 𝑆 so that the return from the portfolio is 𝑅 = 𝑤𝑅_𝑠 + (1 − 𝑤)𝑅_𝑇 . The value of 𝑤 which minimizes 𝑉𝑎𝑟(𝑅) is _____(round off to 2 decimal places)

A number 𝑥 is randomly chosen from the set of the first 100 natural numbers. The probability that 𝑥 satisfies the condition \(𝑥 + \frac{300}{𝑥} > 65\) is ______ (round off to 2 decimal places).