i want help of you in 2 questions
if the s.d. of the first n natural no. is 2, then what is the value of n?
2) the mean and s.d of a b and 2 are 3 and 1 respectively.then what is the value of ab
plz. reply early its solution
thanks in advance
ROSHAN PAUL JOSEPH
(CA Final student)
(311 Points)
Replied 02 June 2011
2) the mean and s.d of a b and 2 are 3 and 1 respectively.then what is the value of ab
given, mean = 3
implies that
(a+b+2)/3=3
so, a+b+2=3*3
a+b=7 -------------------- eqn (1)
given, s.d =1, implies variance = 1*1
i.e, variance, (a-m)2+(b-m)2+(2-m)2 = 1 ; here m, mean =3
{(a-3) 2+(b-3) 2+(2-3) 2 }/3= 1
a2 -6a+9+ b2 -6b+9+1=3
a2 + b2 -6(a+b)=3-19
a2 + b2 -6*7=3-19 from eqn (1)
a2 + b2 = 26 ……. (42-16)
(a+b)2 = a2 + b2+2ab
therefore; 2ab = 7 2 -26
ab = 23/2
ROSHAN PAUL JOSEPH
(CA Final student)
(311 Points)
Replied 02 June 2011
1.if the s.d. of the first n natural no. is 2, then what is the value of n?
n=7
ROSHAN PAUL JOSEPH
(CA Final student)
(311 Points)
Replied 02 June 2011
[{1 – (n+1)/2} 2 +{2 – (n+1)/2} 2 +{3 – (n+1)/2} 2 +…….+{n – (n+1)/2} 2 ]/n = 4
[12 +22 +32 +….+ n2 ] + 2(n+1)/2{1+2+3+…+n}+ n*(n+1)2/22 =4n
n(n+1)(2n+1)/6 – {2(n+1)/2}*n(n+1)/2 + n(n+1)2/4 =4n
n(n+1)/2 { (2n+1)/3- (n+1)/2 + (n+1)/2 } =4n
(n+1) {4n+2-3n-3} / 6 =4*2
(n+1) (n-1) =8*6
n2 - 1 =48
therefore, n=7
ROSHAN PAUL JOSEPH
(CA Final student)
(311 Points)
Replied 03 June 2011
1. f the s.d. of the first n natural no. is 2, then what is the value of n?
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