For a binomial variate X with parameters n=5 and p= 3 4 , if = 1 9 P(X 3) and =P(X 2) , then 256( - )=

Step-by-step solution

For binomial variate n=5, p= 3 4 So, q=1- 3 4 = 1 4 aligned & Now, = 1 9 p(x 3) & = 1 9 [ ^5 C₃ ( 3 4 )^3 ( 1 4 )^2+ ^5 C₄ ( 3 4 )^4 ( 1 4 )+ ^5 C₅ ( 3 4 )^5 ] & = 1 9 [10 27 4^5 +5 81 4^5 + 243 4^5 ]= 1 9 [ 270 4^5 + 405 4^5 + 243 4^5 ] & = 1 9 [ 918 4^5 ]= 102 4^5 = 102 1024 and B=P(x 2) & = ^5 C₀ ( 3 4 )^0 ( 1 4 )^5+ ^5 C₁ ( 3 4 )^1 ( 1 4 )^4+ ^5 C₂ ( 3 4 )^2 ( 1 4 )^3 & =1 1 4^5 +5 3 4^5 +10 9 4^5 = 1+15+90 4^5 = 106 1024 & Now, 256( - )=256 ( 106 1024 - 102 1024 ) & =256 4 1024 =1 aligned