Let \( a_1, a_2, \ldots, a_{10} \) be \( 10 \) observations such that \( \displaystyle \sum_{K=1}^{10}a_k=50 \quad and \sum_{\forall\, k < j} a_k \cdot a_j = 1100 \). Then the standard deviation of \( a_1, a_2, \ldots, a_{10} \) is equal to:
From a lot of \( 12 \) items containing \( 3 \) defectives, a sample of \( 5 \) items is drawn at random. Let the random variable \( X \) denote the number of defective items in the sample. Let items in the sample be drawn one by one without replacement. If variance of \( X \) is \( \dfrac{m}{n} \), where \( \gcd(m,n)=1 \), then \( n-m \) is equal to ______.
