Answer to Question #155874 in Statistics and Probability for Devansh Upadhyay

Question #155874

Two coins tossed simultaneously.A person receive Rs.8 each head and losses Rs.10 for each tail.Find expected value of the amount


1
Expert's answer
2021-01-18T15:10:08-0500

Two coins tossed simultaneously. Let SS be the sample space .

Then SS== {HH,HT,TH,TTHH,HT,TH,TT }

Let us define a random variable X:SRX:S\to R is defined by

X(a)=X(a)= Net amount gain , aS\forall a\in S

Then, X(HH)=16,X(HT)=2,X(TH)=2,X(TT)=20X(HH)=16,X(HT)=-2,X(TH)=-2,X(TT)=-20 .

And probability of each point XX is given below,

P(X=16)=14,P(X=2)=12,P(X=20)=14P(X=16)=\frac{1}{4},P(X=-2)=\frac{1}{2},P(X=-20)=\frac{1}{4}

Now let us draw a table of distribution function as follows




Then E(X)=Σxi.P(xi)E(X)=\Sigma x_i.P(x_i)

=(16×14)+(2×12)+(20×14)=(16×\frac{1}{4})+(-2×\frac{1}{2})+(-20×\frac{1}{4})

=(415)=(4-1-5) =2=-2

Therefore expected value of amount is (2).(-2).




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