List of top Statistics for Economics Questions asked in Indian Institute Of Technology Joint Admission Test for MSc

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?

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?

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

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).

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).

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

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).

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,

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 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 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 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 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 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?

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

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

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?

Which of the following CORRECTLY defines the relationship between the variances of sample means for simple random samples drawn with and without replacement from a normal population?

In the hypothesis testing, which of the following defines the size of power of the test?

Suppose that two random samples of sizes n1, and n2 are selected without replacement from two binomial populations with means = \(\mu_1= n_1p_1, \,\,\,\mu_2= n_2p_2,\) and variances \(σ_1 ^2 = n_1p_1q_!, \,\,\,σ_2^2 = n_2p_2q_2\) , respectively. Let the difference of sample proportions $\overline{P_1} $ and $\overline{P_2} $ approximate a normal distribution with mean ($p_1 - p_2$). Then the standard deviation of the difference of sample proportions  $\overline{P_1} $ and $\overline{P_2} $, is

The probability of getting head in a toss of a biased coin is ⅔ . Let the coin be tossed three times independently. Then the probability of getting head in the first two tosses and tail in the final toss is

Which of the following is NOT correct regarding R-squared ($R^2$) and Adjusted R-squared ($\overline{R^2}$)?

Let \(X \sim N(\mu X, \sigma _X ^2)\) and \(Y \sim N(\mu _y, \sigma _y ^2)\) Which of the following is/are NOT correct?