wiz-icon
MyQuestionIcon
MyQuestionIcon
6
You visited us 6 times! Enjoying our articles? Unlock Full Access!
Question

The random variable takes the values 1,2,3, .........., m. If P(X = n) = 1m to each n, then the variance of X is

A
(m+1)(2m+1)6
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
m2112
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
m+12
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
m2+112
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B m2112
E(x)=mi=1x1Pi=(11m+22m+31m+....m1m)
=(1+2+3+...m)1m
=m(m+1)21m
=(m+1)2
E(x2)=mi=1x2ipi=(121m+222m+....m21m)
=(12+22+....m2)1m
=m(m+1)(2m+1)61m
=(m+1)(2m+1)6
var(x)=E(x2)[E(x)]2
=(m+1)(2m+1)6(m+1)24
=(m+1)(4m+23m3)12
=(m+1)(m1)12
=m2112

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Functions
QUANTITATIVE APTITUDE
Watch in App
Join BYJU'S Learning Program
CrossIcon