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3 years ago

Y=-1/4x+2 slope on a graph

Mathematics

2 answers:

Alex17521 [72]3 years ago

3 0

In this form, slope is simply the coefficient in front of <em>x.</em> Therefore, the slope of this graph is -1/4

irina1246 [14]3 years ago

3 0

Simply go up 2 on the y intercept , then once you've marked that on the graph, go down 1 over 4 since it's a negative slope and your set .

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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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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)

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$\int_{0}^b \frac{1}{1-r}dr=-ln(1-b)$

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

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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