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tino4ka555 [31]

3 years ago

5

Which is the best estimate of 59.4 x 0.28?

1 answer:

JulijaS [17]3 years ago

8 0

<h2><u>PLEASE MARK BRAINLIEST!</u></h2>

Answer:

59.4 * 0.28 = 59 * 0.3

Step-by-step explanation:

59 * 0.3 = ?

59 * 0.3 = 17.7

Your answer is 17.7.

I hope this helps!

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Show that if X is a geometric random variable with parameter p, then

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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:

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

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What is a simplified eCarlotta thinks that 3y + 5y3 is the same as 8y4. Which statement shows that it is NOT the same?Xpression

stira [4]

Questions:

(a) What is a simplified expression for (x + y) – (x – y)?

(b) Carlotta thinks that $3y + 5y^3$ is the same as $8y^4$ . Which statement shows that it is NOT the same?

Answer:

$(x + y) - (x - y) =2y$

$3y + 5y^3 \ne 8y^4$

Step-by-step explanation:

Solving (a):

Given

$(x + y) - (x - y)$

Required

Simplify

$(x + y) - (x - y)$

Open brackets

$(x + y) - (x - y) = x + y - x + y$

Collect Like Terms

$(x + y) - (x - y) = x - x+ y + y$

$(x + y) - (x - y) = y + y$

$(x + y) - (x - y) =2y$

Solving (b):

Given

$3y + 5y^3$ and $8y^4$

Required

Which expression shows they are not the same

The expression that shows this is:

$3y + 5y^3 \ne 8y^4$

Take for instance; y=2

Substitute 2 for y in $3y + 5y^3 \ne 8y^4$

$3*2 + 5*2^3 \ne 8*2^4$

Evaluate all exponents

$9 + 5*8 \ne 8*16$

$9 + 40 \ne 128$

$49 \ne 128$

The above expression supports $3y + 5y^3 \ne 8y^4$

5 0

2 years ago