Search for: If a variable X takes values 0, 1, 2, … , n with frequencies proportional to the binomial coefficients nC0,nC1,nC2,…,nCn, then the Var(X) is If a variable X takes values 0, 1, 2, ... , n with frequencies proportional to the binomial coefficients nC0,nC1,nC2,…,nCn, then the Var(X) is An2−112Bn2Cn4Dnone of these Fill Out the Form for Expert Academic Guidance!l Grade ---Class 1Class 2Class 3Class 4Class 5Class 6Class 7Class 8Class 9Class 10Class 11Class 12 Target Exam JEENEETCBSE +91 Preferred time slot for the call ---9 am10 am11 am12 pm1 pm2 pm3 pm4 pm5 pm6 pm7 pm8pm9 pm10pm Please indicate your interest Live ClassesBooksTest SeriesSelf Learning Language ---EnglishHindiMarathiTamilTeluguMalayalam Are you a Sri Chaitanya student? NoYes Verify OTP Code (required) I agree to the terms and conditions and privacy policy. Solution:We have,X¯=0×nC0×+1×nC1+2×nC2+…+n×nCn nC0+nC1+nC2+…+nCn⇒ X¯=∑r=0n r×nCr∑r=0n nCr⇒ X¯=12n∑r=1n r×nrn−1Cr−1 ∵∑r=0n nCr=2n; nCr=nrn−1Cr−1 ⇒ X¯=n2n∑r=1n n−1Cr−1⇒ X¯=n2n2n−1=n2 ∵∑r=1n n−1Cr−1=2n−1and, 1N∑fixi2=12n∑r=0n r2nCr ⇒1N∑fixi2=12n∑r=0n {r(r−1)+r}nCr⇒ 1N∑fixi2=12n∑r=0n r(r−1)nCr+∑r=0n rnCr⇒ 1N∑fixi2=12n∑r=2n r(r−1)nr×n−1r−1n−2 +∑r=1n Cr−2rnn−1rCr−1⇒ 1N∑fixi2=12nn(n−1)∑r=2n n−2Cr−2+n∑r=1n n−1Cr−1⇒ 1N∑fixi2=12nn(n−1)2n−2+n⋅2n−1 =n(n−1)4+n2∴ Var(X)=1N∑fixi2−X¯2=n(n−1)4+n2−n24=n4 Related content Oppositional Defiant Disorders Good Friday Wishes CBSE Class 9 Physics Motion Worksheet Autism Spectrum Disorder Sine and Cosine Waves Hindu Festivals List 2024 JEE Main Eligibility Criteria 2024 Session 2 (Released), Age Limits, Qualifying Marks, and Important Factor MCQs on Plant Hormones Class 10 5 Reasons To Choose The Commerce Stream After 10th Fl Words