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Julli [10]
2 years ago
6

g: Consider the following game. A coin is flipped. If it lands tails we stop playing and winnothing. If it lands heads we spin a

wheel with numbers from1to100, each with equalprobability. We get the amount of money written on the weel and we play again (i.e. weflip the coin again). LetWbe our total winnings from all tosses of the coin. FindE[W]andVar(W).
Mathematics
1 answer:
galben [10]2 years ago
5 0

Answer:

E[W] = $25 (assuming the currency is in dollars)

Var(W) = 1041.67

Step-by-step explanation:

Probability of winning first starts with the coin toss.

For a win, the coin needs to land on heads.

Probability of that = 1/2 = 0.5

Then probability of winning any amount = 1/100 = 0.01

Total probability of winning any amount = 0.5 × 0.01 = 0.005

But expected value is given by

E(X) = Σ xᵢpᵢ

where xᵢ is each amount that could be won

pᵢ is the probability of each amount to be won and it is the same for all the possible winnings = 0.005

So,

E(W) = Σ 0.005 xᵢ

Summing from 0 to 100 (0 indicating getting a tail from the coin toss). This could be done with dome faster with an integral sign

E(W) = ∫ 0.005 x dx

Integrating from 0 to 100

E(W) = [0.005 x²/2]¹⁰⁰₀

E(W) = [0.0025 x²]¹⁰⁰₀ = 0.0025(100² - 0²) = 0.0025 × 10000 = $25

Variance is given by

Variance = Var(X) = Σxᵢ²pᵢ − μ²

μ = expected value

We calculate the expression, Σxᵢ²pᵢ which is another sum from 0 to 100

Σxᵢ²pᵢ = Σ 0.005xᵢ²

Σ 0.005 xᵢ² = ∫ 0.005 x² dx

Integrating from 0 to 100

∫ 0.005 x² dx = [0.005 x³/3]¹⁰⁰₀ = [0.1667x³]¹⁰⁰₀ = 0.1667(100³ - 0³) = 1666.67

Var(W) = 1666.67 - 25² = 1666.67 - 625 = 1041.67.

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I need help please please
miv72 [106K]

Answer:

The value of x is 7.

Step-by-step explanation:

First, you have to make the left side into 1 fraction by making the denormintor the same and make it into simplest form :

\frac{x}{3}  +  \frac{x}{6}

=  \frac{x \times 2}{3 \times 2}  +  \frac{x}{6}

=  \frac{2x}{6}  +  \frac{x}{6}

=  \frac{2x + x}{6}

=  \frac{3x}{6}

=  \frac{x}{2}

Next you have to multiply both sides by 2 in order to make x the subject :

\frac{x}{2}  =  \frac{7}{2}

\frac{x}{2}  \times 2 =  \frac{7}{2}  \times 2

x = 7

5 0
3 years ago
Write the equation of the line that has a slope of 2 and passes through the point (-3,4).
Arte-miy333 [17]

Answer:

y = 2x + 10

Step-by-step explanation:

We are given the slope of the line and the coordinates of one point on the line.  Thus, we use the point-slope formula y - k = m(x - h).  Here m = 2, h = -3 and k = 4.  Therefore we have:

y - 4 = 2(x + 3)

which can be rewritten as y = 2x + 6 + 4, or y = 2x + 10 (Answer D)

4 0
3 years ago
Answer the 5 questions Listed below Please Show your Work
Zolol [24]
(6 1/3) / (5/6) = (19/3) / (5/6) = 19/3 * 6/5 = 114/15 = 38/5

3 - 7^2 + 3 * 4^2
3 - 49 + 3 * 16
3 - 49 + 48
- 46 + 48
2

(7b - 2) / (-a + 1)....a = -2, b = 3, c = -1/3
where is he c in this equation ? Because if I just use a and b, my answer is not an answer choice

(7b - 10) / (a - 1)...a = -1, b = 5, c = -2/3
same as before...where is the c in this equation

V = (pi) r^2* h
V = (pi)(5^2)(7)
V = (pi)(25)(7)
V = 175(pi)








5 0
3 years ago
What is 8 and 4/25 and as a mixed fraction or mixed number.
Sphinxa [80]

Answer:

Improper fraction for 8 4/25 is 204/25

Step-by-step explanation:

The numbers in the mixed fraction are defined as follow

8 = whole number

4 = numerator

25 = denominator

 Multiply the whole number by the denominator

8 × 25 = 200

Add the product from Step 1 to the numerator

200 + 4 = 204

Write answer from Step 2 over the denominator

204/25

The mixed number 8 4/25 converted to improper fraction is therefore :

3 0
3 years ago
A boat is heading towards a lighthouse, whose beacon-light is 136 feet above the
alexandr1967 [171]

The distance between the points A to B is 899.9 feet. After rounding off the  nearest integer we get 900 feet as the final answer.

Given we know that CD is perpendicular to AD.

The distance between CD is 139 feet.

As from points A the boat's crew measure the angle of elevation to the beacon as 6°

therefore, m∠A = 6°

Another time the angle of elevation is measured from point B which is 19°.

therefore, m∠DBC = 19°

tan 19° = CD/BD

BD = CD/tan19°

BD = 136/tan 19°

now for tan 6° = CD/AD (tangent is opposite over adjacent)

AD = CD/tan 6°

AD = 136/tan 6°

AB = AD ₋ BD

AB = 136/tan 6° ₋ 136/tan 19°

AB = 1295.2 ₋ 395.3

AB = 900 feet

hence the distance from point A to B is 900 feet.

Learn more about Heights and distances here:

brainly.com/question/2004882

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5 0
1 year ago
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