Given:P (X = 1) = P (X = 2) = αP (X= 4)=?P(x=r)= nCr pr qn-rP(x=1)= nC1 p1 qn-1=npqn-1 (1)P(x=2)= nC2 p2 qn-2(2)Equating both equations ,we have:2q = (n-1) p4q2 = (n-1)2 p2P(x=4)= nC4 p4 qn-4For large n; n0So,

Q. 105.0( 1 Vote )

If for a binomial

Class 12th RD Sharma - Volume 2 33. Binomial Distribution

Answer :

Given:

P (X = 1) = P (X = 2) = α

P (X= 4)=?

P(x=r)= ⁿC_r p^r q^n-r

P(x=1)= ⁿC₁ p¹ q^n-1

=npq^{n-1 (1)}

P(x=2)= ⁿC₂ p² q^n-2

⁽²⁾

Equating both equations ,we have:

2q = (n-1) p

4q² = (n-1)² p²

P(x=4)= ⁿC₄ p⁴ q^n-4

For large n; n

So,

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