31.

For a poisson variate X, if P(X = 2) = 3P(X = 3), then the mean of X is :

• 1

• $\frac{1}{2}$

• $\frac{1}{3}$

• $\frac{1}{4}$

The mean and standard deviation of a binomial varate X are 4 and $\sqrt{3}$ respectively. Then, P(X $\ge$ 1) is equal to

• $1 - {\left(\frac{1}{4}\right)}^{16}$

• $1 - {\left(\frac{3}{4}\right)}^{16}$

• $1 - {\left(\frac{2}{3}\right)}^{16}$

• $1 - {\left(\frac{1}{3}\right)}^{16}$

If m and σ² are the mean and variance of the random variable X, whose distribution is given by

X = x	0	1	2	3
P(X = x)	$\frac{1}{3}$	$\frac{1}{2}$	0	$\frac{1}{6}$

Then

• m = σ² = 2

• m = 1, σ² = 2

• m = σ² = 1

• m = 2, σ² = 2

If X is a bmomial variate with the range {0, 1, 2, 3, 4, 5, 6} and P(X = 2) = 4P(X = 4), then the parameter p of X is

• $\frac{1}{3}$

• $\frac{1}{2}$

• $\frac{2}{3}$

• $\frac{3}{4}$

The mean of four observations is 3. If the sum of the squares of these observations is 48, then their standard deviation is

• $\sqrt{7}$

• $\sqrt{2}$

• $\sqrt{3}$

• $\sqrt{5}$

The arithmetic mean of the observations 10, 8, 5, a, b is 6 and their variance is 6.8, then ab is equal to

• 6

• 4

• 3

• 12

If the median of the data 6, 7, x - 2, x, 18 and 21 written in ascending order is 16, then the variance of that data is

• $30\frac{1}{5}$

• $31\frac{1}{3}$

• $32\frac{1}{2}$

• $33\frac{1}{3}$

If the mean of 10 observations is 50 and the sum of the squares of the deviations of the observations from the mean is 250, then the coefficient of variation of those observations is

• 25

• 50

• 10

• 5

The variance of the first 50 even natural numbers is

• $\frac{833}{4}$

• 833

• 437

• $\frac{437}{4}$

If the mean and variance of a binomial distribution are 4 and 2 respectively, then the probability of 2 successes of that binomial variate X, is

• $\frac{1}{2}$

• $\frac{37}{256}$

• $\frac{219}{256}$

• $\frac{7}{64}$