In a series of 2n observations, half of them equals a and remaining half equal -a. If the standard deviation of the observation is 2, then |a| equal to

Solution :

In the 2n observations, half of them equals a and remaining half equal -a. Then, the mean of total 2n observations is equal to 0.

\(\therefore\)   SD = \(\sqrt{\sum(x – \bar{x})^2\over N}\)

\(\implies\)  4 = \(\sum{x^2}\over 2n\)

\(\implies\)  4 = \(2na^2\over 2n\)

\(\implies\)  \(a^2\) = 4

\(\therefore\)   a = 2


Similar Questions

The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, then P(X = 1) is

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observation of the set is increased by 2, then the median of the new is

The mean and the variance of a binomial distribution are 4 and 2, respectively. Then, the probability of 2 success is

The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is

A random variable X has poisson distribution with mean 2. Then, P(X > 1.5) equal to

Leave a Comment

Your email address will not be published. Required fields are marked *

Ezoicreport this ad