(5)
X~B(2,p)
P(X≥1)=8/9
1-P(X=0)=8/9
1-(1-p)^2 =8/9
2p-p^2 =8/9
9p^2-18p+8=0
(3p-2)(3p-4)=0
p=2/3 or 4/3 (rej)
ie
p=2/3
Y~ B(4,p)~B(4,2/3)
P(Y≥1)
=1-P(Y=0)
=1-(1-2/3)^4
=1- 1/81
=80/81
(9)
F(X)
=0 , x<0
=x/2 , 0≤x<2
=1 , x≥2
P(X<1/2)
=F(1/2)
=1/4
X~B(2,p)
P(X≥1)=8/9
1-P(X=0)=8/9
1-(1-p)^2 =8/9
2p-p^2 =8/9
9p^2-18p+8=0
(3p-2)(3p-4)=0
p=2/3 or 4/3 (rej)
ie
p=2/3
Y~ B(4,p)~B(4,2/3)
P(Y≥1)
=1-P(Y=0)
=1-(1-2/3)^4
=1- 1/81
=80/81
(9)
F(X)
=0 , x<0
=x/2 , 0≤x<2
=1 , x≥2
P(X<1/2)
=F(1/2)
=1/4
