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.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1

the answer would be 484

step-by-step explanation:

just multiply 0.484 times 1,000 (formula)