suppose X1, X2 is a random sample of size n = 2 from a population distribution....

Question

Question

suppose X1, X2 is a random sample of size n = 2 from a population distribution.

T 0 1 2 P(x) 0.2 0.5 0.3

i) compute P(X1=X2)

ii) what is the probability that the sample mean is less than 1.5?

Answer 1

Answer #1

i) P(X1=X2) =P(X1=0,X2=0)+P(X1=1,X2=1)+P(X1=2,X2=2) =0.2*0.2+0.5*0.5+0.3*0.3 =0.38

ii) probability that the sample mean is less than 1.5

=P((X1+X2)/2 <1.5)=P(X1+X2<3) =P(X1=0,X2=0)+P(X1=0,X2=1)+P(X1=0,X2=2)+P(X1=1,X2=0)+P(X1=1,X2=1)+P(X1=2,X2=0)

=0.2*0.2+0.2*0.5+0.2*0.3+0.5*0.2+0.5*0.5+0.3*0.2

=0.61

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Answer 2

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