Question

The correlation between X and Y cov (Xy) var (X)var(Y O B. O c. O D. is given by corr (X.Y) is the covariance squared. can be calculated by dividing the covariance between X and Y by the product of the two standard deviations. cannot be negative since variances are always positive.

Answer 1

1) We known that correlation between two variables X and Y

$corr(X,Y)=\frac{cov(X,Y)}{SD(X)SD(Y)}$

SD= standard deviation

So, option C is correct.

2) We known that the distribution of $\bar{Y}$ is, $N(\mu_Y, \frac{\sigma^2_Y}{n})$

$V(\bar{Y})= \frac{\sigma^2_Y}{n}$

So as the sample size increases the variance tends to 0 (decreases).

We know that a normal distribution is symmetric about its mean, so if the variance decreases then the values ($\bar{Y}$) will be more concentrated towards the mean.

Option B is correct