I have 2 questions. Can you see the first page?

Mathematics

1 answer:

kari74 [83]1 year ago

3 0

EXPLANATION :

From the problem, 10 cups of basil are needed to make 5 jars of pesto.

So we can say that 2 cups are needed to make 1 jar of pesto.

The ratio is 2 : 1

From the options, option B satisfies with this condition.

2 cups is to 1 Jar

4 cups is to 2 Jars

10 cups is to 5 Jars

a. The answer is B.

b. To graph, plot the points from option B with (basil, pesto)

(2, 1)

(4, 2)

and (10, 5)

The graph will be :

c. To make 4 jars of pesto, we need to locate y = 4 for pesto then match it with the x-coordinate which is the number of cups of basil.

The new point is (8, 4), so to make 4 jars of pesto, you will need 8 cups of basil.

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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: