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4 years ago

Help me solve this by multiplication or linar combination please

Mathematics

1 answer:

patriot [66]4 years ago

4 0

X would be equal to 0 while y would be equal to -1
-20(0)+6(-1)=-6
-10(0)-4(-1)=4

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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

Fed [463]

Answer:

The out put 1. 5

The out put 2. 6

Step-by-step explanation:

What is this sopost to mean?

Srry if that did not helps much I tried my best

Please give me Brainliest

I really need it plz

3 0

4 years ago

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So can anyone help me with #1 and 2 and show work I have no idea what I’m doing

Neporo4naja [7]

Answer:

x = 44*2

x = 62*2

x = 108/2

x = 160/2

12x = 60*2

12x = 120

x = 120/12

5x = 50/2

5x = 25

x = 25/5

3 0

3 years ago

1. What number is 35% of 80?<br>

Stella [2.4K]

Answer: 28

Step-by-step explanation: 80 x 0.35 = 28

6 0

2 years ago

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Is an angle that is greater than 90 degrees is acute True or False

Brilliant_brown [7]

Hey there!

The answer is false. A 90 degree angle is called a right triangle. Any angle less than 90 degree is called an acute angle. Any angle more than 90 degree is called an obtuse angle

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3 years ago

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