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Mnenie [13.5K]
3 years ago
15

What is the answer to this question Possible Answers A.4.5 B.5.4 C.9.1 D10.9

Mathematics
1 answer:
vova2212 [387]3 years ago
7 0
The answer is B. 5.4
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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
The graph is of y = f(x) is shown below. What are all of the real solutions of f(x) = 0?
Reika [66]

The real solutions of f(x) = 0 is; x = -8, 0 and 4

<h3>How to find the roots of a polynomial graph?</h3>

When talking about real solutions of a polynomial, we are simply referring to the values of x that make the polynomial f(x) = 0.

Now, in a polynomial graph as attached, the real solutions are the roots and they are the values of x where the curve crosses the x-axis.

From the given graph, the real solutions are at x = -8, 0 and 4

Thus, we conclude that the real solutions of f(x) = 0 is; x = -8, 0 and 4

Read more about Polynomial roots graph at; brainly.com/question/14625910

#SPJ1

8 0
1 year ago
Can somebody help answer this right plz!!!! (Grade7math)<br> (WILL MARK BRAINLIEST) <br> Thanks :)
notka56 [123]

Answer:

396°

Step-by-step explanation:

Difference = 357 -(-39) = 357+38 = 396°

8 0
3 years ago
Read 2 more answers
Help please! I’ll give you brainlist
11111nata11111 [884]

Answer:

1,007 calories in total

Step-by-step explanation:

8 0
3 years ago
What is the solution to the system of equations below? Please show work.
snow_tiger [21]

Answer:

2)     (0,-3)

Step-by-step explanation:

hello :

put x=0 and y= -3 in this system !

Y = 3/4x - 3

3x - 4y = 12

- 3 = 3/4(0) - 3  means : -3 = -3 ......true

3(0) - 4(-3) = 12  means : 12= 12 ......true

4 0
2 years ago
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