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.

both equations and proportions are better.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.