Question

1. A fair coin will be tossed 200,000 times. Let X denote the number of Tails. (a) What is the expected value and the standard deviation of X? (b) Consider a game in which you have to pay $5 in order to earn $log10(X) when X > 0. Is this a fair game? If not, your expected profit is positive or negative?

Answer #1

Here we have X: number of tails occurs in 200000 times coin tossed.

a) to obtain the E(X) and SD(X) run the following code in R

**x=seq(from=1, to=200000, by=1)
n=length(x)
n
expect=sum(x*(x/n))
expect
var= sum((x-m)^2*(x/n))
SD=sqrt(var)
SD**

We get the following values

**E(X)= 13333433334**

**SD(X)= 4.21637e+12**

**b) Since we in order to earn the Log10(X) we have to pay
$5 , which results into paying high amount so this will lead to
negative profit. Hence not a fair game**

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