Let a_1 ,a_2 , …a_10 be 10 observations such that _k=1^10 0.05ema_k=50 and _ ∀k

Question

Let a_1 ,a_2 , …a_10 be 10 observations such that _k=1^10 0.05ema_k=50 and _ ∀k<j 0.05ema_k a_j=1100. Then the standard deviation of a_1 ,a_2 , … ,a_10 is equal to :

Accepted Answer

Correct answer: B. (b) _k=1^10 0.05ema_k=50a_1+a_2+ …+a_10=50 … . (i ) _ ∀k<j 0.05ema_ka_j=1100 … ( ii ) Ifa_1+a_2+ …+a_10=50 .(a_1+a_2+ …+a_10)^2=2500 ⇒ _i=1^10 0.05ema_i^2+2 _k<j 0.05ema_ka_j=2500 ⇒ _i=1^10 0.05ema_i^2=2500-2 (1100 ) _i=1^10 0.05ema_i^2=300 , Standard deviation ^ ' = a_i^210- ( a_i10 )^2= 30010- ( 5010 )^2 = 30-25= 5

$Let a_{1}, a_{2}, \dots a_{10} be 10 observations such that \sum_{k = 1}^{10} a_{k} = 50 and \sum_{\forall k < j} a_{k} \cdot a_{j} = 1100 . Then the standard deviation of a_{1}, a_{2}, \dots, a_{10} is equal to :$

Solution

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