Page 148 - Math Grade 12 (Advance)

PROEUS DARA

= aL,xxP(X=x) = aE(X) tl:hru L,xxP(X=x) = E(X) '1

3. E(aX +b) = L,[(ax +b) x P(X = x)]

= Laxx P(X = x) + L,bx P(X = x)

= aL,x x P(X = x) + bLP(X = x) = aE(X) + b '1

4. E(f (X) + f (X)] = L,{[f (x) + f x] x P(X = x)}
1 2 1 2
= L/ (x) X P(X = x) + L,f (x) X P(X = x)
1 2
= E(f (X)] + E[f (X)]
2
1
i':H:Hsg E[f (X) + f (X)] = E[f (X)] + E(f (X)] '1
2
1
2
u 1
X I 2 3
cf IQI 0
HS!=i'l§Si':HHtHn P(X = x) tHmg X= 1' 2, 3 '1
I I P(X = x) 0.2 0.3 0.5
n. l=iMS'l £(3)

2. 5E(X) + 2
2
l=i. E(X +4) '1

.,
t1Ii1t!! :
n. £(3) = 3

2. ~1JilLn1~n E(X) tlis
u
E(X) = L,xx P(X = x) = 1(0.2) + 2(0.3) + 3(0.5) = 2.3

5E(X) + 2 = 5(2.3) + 2 = 13.5 '1
2 2
l=i. E(X + 4) = E(X ) + £(4)
2 2 2 2 2
tn £(4) = 4 Sb E(X ) = L,x xP(X=x) = 1 (0.2)+2 (0.3)+3 (0.5) = 5.9
2
!::Wtsg E(X +4)=5.9+4 = 9.9 '1
u
LuRug : Htd~tcrtlSJ x 'i:flSH~l=i'l§Stllh~tntymu P(X = O) = o.o5 ,
u
P(X = l) = 0.45 Sb P(X = 2) = 0.5 '1 l=iMS'l

2
n. 11 = E(X) l=i. E(5X +2X-3) '1

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