Afair 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 and explanation:

Given : A fair coin will be tossed 200,000 times. Let X denote the number of Tails.

To find :

(a) What is the expected value and the standard deviation of X?

Given that total number of tosses is n=200000

Probability of getting tail in single toss is p=0.5

Expected value is given by,

Standard deviation is given by,

(b) Consider a game in which you have to pay $5 in order to earn when X > 0. Is this a fair game? If not, your expected profit is positive or negative?

We have to pay $5 to get

Minimum number of tails required to get $5 is 100000 .

Since, we get X=100000 with Probability 0.5 and for winning we need more number of tosses.

Probability of losing is more than profit hence it's biased test .

As expected number of tails =100000

So profit is given by,

Therefore, The profit is zero.

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step-by-step explanation:

step-by-step explanation:

when the line is solid:

when the line is dashed:

this > inequality sign means:

this < inequality sign means:

this > inequality sign means:

this < inequality sign means:

about the problem:

srry i'm not done ! i'll