If the variable takes values 0,1,2,3,...,n with frequencies, proportional to nC0,nC1,nC2,...,nCn respectively, then variance is
A
n4
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
n3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
2n5
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
None of these
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is An4 xi=0,1,2,...,n fi=nC0,nC1,nC2,...,nCn respectively. Variance =∑x2ifi∑fi−(∑xifi∑fi)2 Now we can solve it one by one (∑xifi∑fi)=⎛⎜
⎜
⎜
⎜⎝n∑r=0rnCrn∑r=0nCr⎞⎟
⎟
⎟
⎟⎠=12n(n∑r=0rnCr) =12n(n∑r=0rnrn−1Cr−1)=n2n(n∑r=0n−1Cr−1) =n2n(2n−1)=n2