Random variable X has a distribution:
P(x=0)=0.2 ; P(x=1)=0.3 ; P(x=2)=0.1 & P(x=3)=0.3 ; P(x=4)=0.1.
Find: a) E(x) and Var(x)
b) Find Fx(Xo)
c) Find quantile of order 1/4 and median
d) Find P(2<=x<=4)
given that
P(x=0)=0.2 ; P(x=1)=0.3 ; P(x=2)=0.1 & P(x=3)=0.3 ; P(x=4)=0.1
a)
E(X)=0.2*0+1*0.3+2*0.1+3*0.3+4*0.1
=1.8
E(X2)=0.2*02+12*0.3+22*0.1+32*0.3+42*0.1
=5
Now
Var(X)=E(X2) -[E(X)]2 =5-1.82=1.76
b)
now
c)
quantile of order 1/4th is 1st quartile that
is P(X<x) =0.25
since
P(X=0) =0.2
so it will take values between 0 and 1
here
P(X<1)=0.5
Hence 1 is median
d)
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