List of top Questions asked in ICAR AIEEA (PG)- 2023

Two independent variables have mean 5 and 10 and variances 5 and 9 respectively. Obtain the correlation between $Y_1 = 3X_1 + 4X_2$ and $Y_2 = 3X_1 - X_2$

If the sample means for each of the k treatment groups were identical, what would be the observed value of the ANOVA test statistic?

In Standard normal distribution, the value of median is _______

In a Binomial Distribution, if 'n' is the number of trials and 'p' is the probability of success, then the standard deviation is given by?

Out of these, which is not a probability sampling?

If the mean and variance of a variable following binomial distribution are 16 and 8 respectively, then find $P(X > 0)$.

The point of intersection of the 'less than' and the 'more than' ogive corresponds to

Which of the following measures of central tendency is not affected by presence of outliers?

For a discrete data set when all the values are not same then the relationship between mean deviation about mean (MD) and standard deviation (SD) is

If all frequencies of classes are same, the value of chi-square ($\chi^2$) is:

A random variable X is normally distributed with zero mean and unit variance. The variance of $X^2$ is

The coefficient of variation of Poisson distribution with mean 9 is

Let X be a random variable with p.d.f. f(x) =6x(1-x), 0\(\le\) x \(\le\)1. Determine the value of b such that P(X < b)=P(X > b).
1. \(\frac{1}{2}\)
2. \(\frac{1 \mp \sqrt{3}}{2}\)
3. 0
4. \(\frac{1}{3}\)

A person speaks truth 4 out of 5 times. A die is tossed. He reports that there is a six. What is the chance that actually there was six?
1. \(\frac{4}{9}\)
2. \(\frac{5}{9}\)
3. \(\frac{1}{9}\)
4. \(\frac{1}{3}\)

If X and Y are independent Poisson variates, What is the distribution of \(\frac{X}{X+Y}\)?
1. Binomial distribution
2. Poisson distribution
3. Negative binomial distribution
4. Multinomial distribution

The range of Correlation coefficient is
1. -1 to +1
2. -1 to 0
3. 0 to +1
4. -\(\infty\) to +\(\infty\)

For any discrete distribution, what is the value of $\beta_2$?

The relationship between root mean square deviation (r.m.s.d.) and standard deviation (s.d.) is
1. s.d. = highest value of r.m.s.d.
2. s.d. = least value of r.m.s.d.
3. s.d. = r.m.s.d.
4. s.d. = (r.m.s.d)/2

Let random variables \(X_1, X_2, \dots, X_k\) follows a multinomial distribution with parameter n and \(p_i\) where i= 1, 2,...,k. what is the value of Cov(\(X_i, X_j\))?
1. \(np_ip_j\)
2. \(-np_ip_j\)
3. \(p_ip_j\)
4. \(-p_ip_j\)

A random sample of size 20 from a normal population gives a mean 42 and variance 25. To test that the population standard deviation is 8, the value of test statistics is
1. 7.42
2. 15.62
3. 51.20
4. 55.60

In Simple Random Sampling with replacement (SRSWR), the total no. of samples (with standard notation) will be
1. \(\binom{N}{n}\)
2. \(N^n\)
3. n + N
4. n*N

Given the eight sample values as -4, -3, -3, 0, 3, 3, 4, 4, the value of student's t- test \(H_0: \mu=0\) is:
1. 2.73
2. 0.97
3. 3.30
4. 0.41

If two independent random variable X and Y are binomially distributed with \(n_1=4\), p=(1/3) and \(n_2=5\), p= (1/3) respectively, Find the mode of the distribution of (X+Y).
1. 3, 2
2. 3
3. 3, 4
4. 4

Suppose the correlation coefficient for a pair of 625 random sample is 0.2. Is the value of r significant? Given \(t_{0.05, 623} = 1.96\).
1. Yes, value of r is significant
2. No, value of r is not significant
3. may or may not be significant
4. test is invalid

Let \(\bar{X}\) be the mean of a random variable of size 5 from a normal distribution with \(\mu=0\) and variance \(\sigma^2 = 125\). Determine c so that P(\(\bar{X} < c\)) = 0.90
1. 6.10
2. 6.20
3. 6.30
4. 6.40