Use the data set to answer the question.

Mathematics

2 answers:

vagabundo [1.1K]3 years ago

4 0

Answer:

The only choice showing the correct distribution of frequencies is c.

Step-by-step explanation:

Data Plots

Considering the provided data:

{11,15,8,2,7,10,9,12,11,8,12,3,14,8,2,9}

To produce a data plot, it's convenient to sort the data:

{2,2,3,7,8,8,8,9,9,10,11,11,12,12,14,15}

It's easier now to see the frequency of each data:

# :f

-----

2 :2

3 :1

7 :1

8 :3

9 :2

10:1

11:2

12:2

14:1

15:1

The only choice showing the correct distribution of frequencies is c.

zalisa [80]3 years ago

3 0

The answer is c I 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: