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3 years ago

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Question is down below:

1 answer:

Ivahew [28]3 years ago

7 0

Answer:
b) -1.6

Step-by-step explanation:
-2, -1.8, -1.6, -1.4, -1.2, -1

Hope this helps!

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Show that if X is a geometric random variable with parameter p, then

Lubov Fominskaja [6]

Answer:

$\sum_{k=1}^{\infty} \frac{p(1-p)^{k-1}}{k}=-\frac{p ln p}{1-p}$

Step-by-step explanation:

The geometric distribution represents "the number of failures before you get a success in a series of Bernoulli trials. This discrete probability distribution is represented by the probability density function:"

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

Let X the random variable that measures the number os trials until the first success, we know that X follows this distribution:

$X\sim Geo (1-p)$

In order to find the expected value E(1/X) we need to find this sum:

$E(X)=\sum_{k=1}^{\infty} \frac{p(1-p)^{k-1}}{k}$

Lets consider the following series:

$\sum_{k=1}^{\infty} b^{k-1}$

And let's assume that this series is a power series with b a number between (0,1). If we apply integration of this series we have this:

$\int_{0}^b \sum_{k=1}^{\infty} r^{k-1}=\sum_{k=1}^{\infty} \int_{0}^b r^{k-1} dt=\sum_{k=1}^{\infty} \frac{b^k}{k}$ (a)

On the last step we assume that $0\leq r\leq b$ and $\sum_{k=1}^{\infty} r^{k-1}=\frac{1}{1-r}$ , then the integral on the left part of equation (a) would be 1. And we have:

$\int_{0}^b \frac{1}{1-r}dr=-ln(1-b)$

And for the next step we have:

$\sum_{k=1}^{\infty} \frac{b^{k-1}}{k}=\frac{1}{b}\sum_{k=1}^{\infty}\frac{b^k}{k}=-\frac{ln(1-b)}{b}$

And with this we have the requiered proof.

And since $b=1-p$ we have that:

$\sum_{k=1}^{\infty} \frac{p(1-p)^{k-1}}{k}=-\frac{p ln p}{1-p}$

4 0

3 years ago

In a competition between players X and Y, the first player to win three games in a row or a total of four games wins. How many w

OLEGan [10]

Answer:

The competition can be played in 7 different ways

Step-by-step explanation:

First game : X

Second game : Y

Third game : Y

After that either X or Y can win

<h3>¹Case - 1: Y wins the fourth game:</h3>

The competition ends with Y winning as he/she won 3 games in a row

<h3>Case - 2: X wins the fourth game:</h3>

more games are required to decide the winner

<h3>Sub-case - a: X wins the fifth game:</h3>

more games are required to decide the winner

<h3>²Sub-sub-case - i: X wins the sixth game:</h3>

The competition ends with X winning as he/she won 3 games in a row

<h3>³⁻⁴Sub-sub-case - ii: Y wins the sixth game:</h3>

The competition ends after the seventh game. Whoever wins seventh game wins the competition as he/she would've won 4 games in total by then.

<h3>Sub-case - b: Y wins the fifth game:</h3>

more games are required to decide the winner

<h3>⁵Sub-sub-case - i: Y wins the sixth game:</h3>

The competition ends with Y winning as he/she won 4 games in total

<h3>⁶⁻⁷Sub-sub-case - ii: X wins the sixth game:</h3>

The competition ends after the seventh game. Whoever wins seventh game wins the competition as he/she would've won 4 games in total by then.

∴<u>The competition can be played in 7 different ways</u>

7 0

3 years ago

Which statement is true about the points shown on the number line?

Arlecino [84]

It should be "A"

On the number line, it shows that -4.5 is further and to the right of -2.3.

Hope that helps!

5 0

3 years ago

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What is the product? 8(–1) A. –1.4 B. –8 C. 8 D. 11.2

enot [183]

B: -8
8 times 1 = 8, and since there is a negative in front of the 1 when you are multiplying, it should be -8/

7 0

3 years ago

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A BAKER USED 4 CUPS OF FLOUR TO MAKE 5 BEATLES OF COOKIES. HE USED ???? OF A CUP OF FLOUR TO MAKE 1 BATCH OF COOKIES

zepelin [54]

Answer:

Your answer will be 1.2 cups of flour

or

1 1/5

Step-by-step explanation: I hope this heled, if not let me know and I will get you a better answer! :)

5 0

3 years ago

Read 2 more answers