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3 years ago

In which pair of numbers is the first number of the multiple of the second number?

Mathematics

1 answer:

irina1246 [14]3 years ago

7 0

Your answer would be c. 18,6

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Suppose we play the following game based on tosses of a fair coin. You pay me $10, and I agree to pay you $n 2 if heads comes up

Artyom0805 [142]

Answer:

In the long run, ou expect to lose $4 per game

Step-by-step explanation:

Suppose we play the following game based on tosses of a fair coin. You pay me $10, and I agree to pay you $n^2 if heads comes up first on the nth toss.

Assuming X be the toss on which the first head appears.

then the geometric distribution of X is:

X $\sim$ geom(p = 1/2)

the probability function P can be computed as:

$P (X = n) = p(1-p)^{n-1}$

where

n = 1,2,3 ...

If I agree to pay you $n^2 if heads comes up first on the nth toss.

this implies that , you need to be paid $\sum \limits ^{n}_{i=1} n^2 P(X=n)$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) = E(X^2)$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) =Var (X) + [E(X)]^2$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{1-p}{p^2}+(\dfrac{1}{p})^2$ ∵ X $\sim$ geom(p = 1/2)

$\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{1-p}{p^2}+\dfrac{1}{p^2}$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{1-p+1}{p^2}$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{2-p}{p^2}$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{2-\dfrac{1}{2}}{(\dfrac{1}{2})^2}$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) =\dfrac{ \dfrac{4-1}{2} }{{\dfrac{1}{4}}}$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) =\dfrac{ \dfrac{3}{2} }{{\dfrac{1}{4}}}$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) =\dfrac{ 1.5}{{0.25}}$

$\sum \limits ^{n}_{i=1} n^2 P(X=n) =6$

Given that during the game play, You pay me $10 , the calculated expected loss = $10 - $6

= $4

∴

In the long run, you expect to lose $4 per game

3 0

3 years ago

Solve:<br><br> If Sally can walk 1/3 of a mile in 1/4 of an hour. How far will she walk 2 1/2 hours?

Daniel [21]

The answer is 3 and 1/3 miles

8 0

3 years ago

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The sum of two negative integers is a negative integers

Vaselesa [24]

Answer:

when we add two negative numbers the result will always be a negative number, on adding negative numbers the direction of the move will always be to the left side

hope this helps!

3 0

2 years ago

To simplify expressions, we often ___ like terms.

tekilochka [14]

Answer: combine

Step-by-step explanation:

When you combine like terms, it shortens or simplified the equation

Example: 2x-5+15

Combine actual numbers -5 and 15.

2x+10

6 0

2 years ago

You can spend no more than $100 on a party you are hosting. The cost per guest is $8. What is the greatest number of guests that

spayn [35]

Answer:

the greatest number of guests is 12 guests

Step-by-step explanation:

100÷8=12.5

3 0

3 years ago

Read 2 more answers