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2 years ago

What are the solutions to the equation y = 4x2 + 50 – 6?

Mathematics

2 answers:

krok68 [10]2 years ago

8 0

Y=52
first do 4x2 which is 8 plus 50 is 58 minus 6 is 52.

kifflom [539]2 years ago

5 0

Y = 52

Explanation: 4x2 is 8 and add 50 which is 58 - 6 which is 52

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Answer:

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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:"

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

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

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Lets consider the following series:

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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:

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

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