Question

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

Answer 1

Two coins tossed simultaneously. Let $S$ be the sample space .

Then $S$$=$ {$HH,HT,TH,TT$ }

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

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

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

And probability of each point $X$ is given below,

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

Now let us draw a table of distribution function as follows

Then $E(X)=\Sigma x_i.P(x_i)$

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

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

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