A mosquito is walking at random on the nonnegative number line. She starts at $1$. When she is at $0$, she always takes a step $1$ unit to the right, but, from any positive position on the line, she randomly moves left or right $1$ unit with equal probability. What is the expected number of times the mosquito will visit $0$ before the first time she visits $4$?

Answers

Answer 1

The expected number of times the mosquito will visit 0 before the first time she visits 4 is 3/4 by using concept of probability and geometric series.

Given that repeatedly throwing a fair tetrahedral die, trying to get a 4 (success) before getting a number from 1 to 3 (failure), which follows a geometric distribution.

To find the expected number of visits to 0 before reaching 4, analyze two cases:

success (reaching 4 before 0) and failure (reaching 0 before 4).

By the given data, the probabilities of two cases are:

P(success) p = 1/4,

P(failure)=3/4.

The expected count of failures, X, can be found in terms of success probability p as

[tex]E[X]=\sum_{x=0}^{+\infty}[x(1-p)^xp][/tex]

On substituting p = 1/4 gives:

[tex]E(X) = 0(1/4)+1(3/4)(1/4)+2(3/4)^2(1/4)+3(3/4)^3(1/4)+.........[/tex]

On taking (1/4) gives

[tex]E(X) = 1/4[3/4+(3/4)^2+(3/4)^3+......+\infty]----(1)[/tex]

Consider [tex]3/4+(3/4)^2+(3/4)^3+......+\infty[/tex]

This forms a geometric series tends to infinity and the sum is given by :

[tex]S_\infty = a/(1-r)[/tex]

Here: a= 3/4

r = 3/4

Plugging these values into formula gives:

[tex]3/4+(3/4)^2+(3/4)^3+......+\infty = S_\infty[/tex]

[tex]S_\infty= 3/4/(1-3/4)[/tex]

On subtracting the denominator gives:

= 3/4/(1/4)

On taking reciprocal gives:

= 3/4 * 4

On simplifying gives:

= 3

Substituting these value into given equation 1 gives:

E(X) = 1/4*[3]

On multiplying gives:

E(X) = 3/4.

Therefore, the  expected number of times the mosquito will visit 0 before the first time she visits 4 is 3/4 by using concept of probability and geometric series.

Learn more probability about here:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

P = 2

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Multiply "q" (which is 8) with 8

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I hope this helps. :)

The answer I got was: {{ 2,8}}

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answers

Answer:

The answer is 9

Step-by-step explanation:

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Then subtract 144 from both sides and get 81

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Answers

Answer:

France's GDP is 50 000 times larger than Tuvalu's GDP.

Step-by-step explanation:

Given: Gross Domestic Product (GDP) of France = $2.0 x [tex]10^{12}[/tex]

            Gross Domestic Product (GDP) of Tuvalu = $4.0 x [tex]10^{7}[/tex]

To determine the number of times in which the GDP of France is greater than that of Tuvalu, divide the GDP of France by the GDP of Tuvalu.

[tex]\frac{2.0*10^{12} }{4.0*10^{7} }[/tex] = [tex]\frac{2000000000000}{40000000}[/tex]

           = [tex]\frac{200000}{4}[/tex]

           = 50000

Therefore, France's GDP is 50 000 times larger than Tuvalu's GDP.

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Answers

Answer:

5.35

Step-by-step explanation:

5.31 5.32 5.33 5.34 5.35

The answer will be 5.35

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Answers

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Answers

Answer and explanation:

A rectangle's width is longer than the length

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x can be solved

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Y can be solved

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10x+20y=72-40

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Answers

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Answers

Answer:

21ab-14ac+28a

Step-by-step explanation:

[tex]7a(3b - 2c + 4)\\\\\mathrm{Distribute\:parentheses}\\\\=7a\times \:3b+7a\left(-2c\right)+7a\times\:4\\\\\mathrm{Apply\:minus-plus\:rules}\\\\+\left(-a\right)=-a\\\\=7\times\:3ab-7\times\:2ac+7\times\:4a\\\\Simplify\\\\21ab-14ac+28a[/tex]

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Answers

Answer:

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Answers

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Find the inverse of the function f(x) = 2x - 4

Answers

The correct answer is f^-1(x)=1/2x+2.

1. Substitute y for f(x). ( y=2x+4 )

2. Interchange the variables x and y. ( x=2y-4 )

3. Swap the sides. ( 2y-4=x )

4. Move the constant to the right. ( 2y=x+4 )

5. Divide both sides by 2. ( y=1/2x+2 )

6. Use substitution to substitute f^-1(x) for y.

Thus the inverse is f^-1(x)=1/2x+2

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