List of top Statistical Science Questions asked in ICAR AIEEA (PG)

Which of the following statements is false?

For which values of $x$, the complex numbers $\cos x + i \sin 2x$ and $\sin x - i \cos 2x$ are conjugates of each other?

The Area of triangle whose vertices are iota, $w$ and $w^2$, where $w$ and $w^2$ are non real cube roots of unity, is :

The modulus and argument of complex number $z = \frac{1}{(2\sqrt{3} + 2i)^4}$ is}

The cubic equation $4x^3 + 3x^2 + 2x + 1 = 0$ has:

The pair of values representing two correct regression coefficients in case of simple linear regression is

The number of possible samples of size n out of N population units in simple random sampling without replacement is

If P(A | B) < P(A), then P(B | A) is

In case of Completely randomized design (CRD) which of the following statement is false?

If $X$ and $Y$ are independent Poisson variates with means as 10 and 5 respectively. Then $V(X - 2Y) =$

Given below are two statements
Statement I: For normal distribution, all central moments exist.
Statement II: For normal distribution Mean deviation (MD): Quartile deviation (QD): Standard Deviation (SD) is 10:12:15.
In light of the above statements, choose the correct answer from the options given below

In a completely randomized design with 6 treatments each replicated 3 times, the F-ratio would have degrees of freedom equal to

Given below are two statements
Statement I: Probability of rejecting null hypothesis when it is true is known as level of significance.
Statement II: Probability of rejecting null hypothesis when it is false or alternate hypothesis is true is known as power of the test.
In light of the above statements, choose the correct answer from the options given below

If $X$ follows binomial distribution with parameters 10 and 1/2, then $E(X - 5)^2 =$

Which test will be used in order to see whether the observed phenotypic segregation ratio in $F_1$ generation is 3:1 or not when two hybrids are crossed?

Two lines of regression intersect at

The coefficient of correlation between two variables $X$ and $Y$ is 0.6. Their covariance is 4.8. The variance of $X$ is 9. Then the standard deviation of $Y$ is

The Binomial distribution with probability of success as $p$, will be symmetric if

A group consists of 9 students from 3 disciplines. Out of the 9 students, 4 are from Statistics, 3 are from Economics and 2 are from Chemistry. Three students are selected randomly. What is the probability that, out of the selected students 2 are from Statistics?

A problem in Statistics is given to three students A, B and C whose chances of solving it are 1/2, 3/4 and 1/4 respectively. What is the probability that the problem will be solved if all of them tried independently?

Which one of the following probability mass function is impossible?

Two means are compared using t-test to assess the statistical significance of the difference between two samples. Size of the first sample is 17 and the size of the second sample is 13. How many degrees of freedom are associated with the critical t-value?

In testing of hypothesis, whether a critical region is one sided or two sided depends on

The average of the 7 numbers 7, 9, 12, x, 5, 4, 11 is 9. The missing number is

Testing $H_0: \mu = 0$ vs $H_1: \mu > 0$ is a