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yuradex [85]
3 years ago
6

Need help answers please

Mathematics
1 answer:
Alborosie3 years ago
5 0
No the first one worked not the second one
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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
Help please!!!<br><br><br><br><br><br> ———————-
Marat540 [252]
B is the answer okay
5 0
3 years ago
Read 2 more answers
Andy joins a social networking site. After day three, he has 25 friends; after day eight, he has 40 friends. Write the equation
Allisa [31]

Answer:

Point slope intercept form: The equation for line is given by; y-y_1=m(x-x_1) ......[1] ; where m is the slope and a point (x_1, y_1) on the line.

Let x represents the number of days and y represents the number of friends.

As per the statement:  After day three, he has 25 friends; after day eight, he has 40 friends.

⇒ We have two points i.e,

(3, 25) and (8, 40)

First calculate slope(m);

m = \frac{y_2-y_1}{x_2-x_1}

Substitute the given values we get;

m = \frac{40-25}{8-3}=\frac{15}{5} = 3

now, substitute the given values of m=3 and a point (3, 25) in [1] we get;

y-25=3(x-3)

Using distributive property; a \cdot(b+c) = a\cdot b + a\cdot c

y-25 = 3x - 9

Add 25 on both sides, we get;

y-25+25 = 3x - 9+25

Simplify:

y =3x + 16

if  x = 18 days, then;

y = 3(18) + 16 = 54+16 = 70

Therefore, he will have on day 18, if he continues to add the same number of friends each day is, 70 friends.

7 0
3 years ago
Triangle ABC has side a= 12, b=16, and c=c find the measure of angle a to the nearest whole number
Aleks04 [339]
C would equal 20. because 12 times its self plus 16 times its self equals 400. then I square 400 and  got 20, which equals c 
5 0
3 years ago
Find x, y, and z.<br><br> Multiple choice answers are below!
labwork [276]

Answer:

<u>The correct answer is B. x ≈ 4.5, y = 5, z = 9</u>

Step-by-step explanation:

1. We will use the Pythagorean theorem for solving for x, this way:

x² = 6² - 4²

x² = 36 - 16

x² = 20

x = √20

x = 2 √5 = 4.47 ≈ 4.5

2. For solving for y, we will do it this way:

There are only two possible options: y = 5, included in answer B or y = 9 as it is defined on answer C.

If we review it carefully, we will realize that y = 9 is not accurate because as we can see in the graph y + 4 = z and in this specific case, 9 + 4 ≠ 5 but it's true that 5 + 4 = 9.

<u>Because of this reason, the correct answer is B. x ≈ 4.5, y = 5, z = 9</u>

7 0
3 years ago
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