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1 year ago

What is the expected value for the following probability distribution?

Mathematics

1 answer:

dolphi86 [110]1 year ago

5 0

To calculate the expected value of our dataset, first we need to find the missing probability. The sum of the probabilities of all outcomes must add up to 1

$\sum P(X)=1$

Therefore, 1 minus all the other probability values is going to be P(2).

$1-(0.04+0.05+0.2+0.1)=1-0.75=0.25$

The expected value is given by the sum of every value of the dataset multiplied by its respective probability

$E[X\rbrack=\sum P(x_i)x_i$

Using this formula in our problem, we have:

$\begin{gathered} E[X\rbrack=\sum_{i\mathop{=}1}^5P_i(x_i)x_i \\ =(0.4)\times(0)+(0.05)\times(1)+(0.25)\times(2)+(0.2)\times(3)+(0.1)\times(4) \\ =0+0.05+0.5+0.6+0.4 \\ =1.55 \end{gathered}$

The expected value of this dataset is 1.55.

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Anastaziya [24]

Answer:

$\displaystyle \frac{dy}{dx} = \frac{2x + 2}{x^3}$

Step-by-step explanation:

we would like to figure out the derivative of the following:

$\displaystyle \frac{ { 3x }^{2} - 2x - 1 }{ {x}^{2} }$

to do so, let,

$\displaystyle y = \frac{ { 3x }^{2} - 2x - 1 }{ {x}^{2} }$

By simplifying we acquire:

$\displaystyle y = 3 - \frac{2}{x} - \frac{1}{ {x}^{2} }$

use law of exponent which yields:

$\displaystyle y = 3 - 2 {x}^{ - 1} - { {x}^{ - 2} }$

take derivative in both sides:

$\displaystyle \frac{dy}{dx} = \frac{d}{dx} (3 - 2 {x}^{ - 1} - { {x}^{ - 2} } )$

use sum derivation rule which yields:

$\rm\displaystyle \frac{dy}{dx} = \frac{d}{dx} 3 - \frac{d}{dx} 2 {x}^{ - 1} - \frac{d}{dx} {x}^{ - 2}$

By constant derivation we acquire:

$\rm\displaystyle \frac{dy}{dx} = 0 - \frac{d}{dx} 2 {x}^{ - 1} - \frac{d}{dx} {x}^{ - 2}$

use exponent rule of derivation which yields:

$\rm\displaystyle \frac{dy}{dx} = 0 - ( - 2 {x}^{ - 1 -1} ) - ( - 2 {x}^{ - 2 - 1} )$

simplify exponent:

$\rm\displaystyle \frac{dy}{dx} = 0 - ( - 2 {x}^{ -2} ) - ( - 2 {x}^{ - 3} )$

two negatives make positive so,

$\displaystyle \frac{dy}{dx} = 2 {x}^{ -2} + 2 {x}^{ - 3}$

<h3>further simplification if needed:</h3>

by law of exponent we acquire:

$\displaystyle \frac{dy}{dx} = \frac{2 }{x^2}+ \frac{2}{x^3}$

simplify addition:

$\displaystyle \frac{dy}{dx} = \frac{2x + 2}{x^3}$

and we are done!

5 0

3 years ago

What does n = in 10=6+n/2

Pani-rosa [81]

Answer:

n = 8

Step-by-step explanation:

10=6+n/2

Switch sides

6 + n/2 = 10

Subtract 6 from both sides

6 + n/2 -6 = 10-6

Simplify

n/2 = 4

Multiply both sides by 2

2n/2 = 4 times 2

n = 8

Hope this helps!

8 0

3 years ago

The Marked price of an article is rupees 5000 .This price is 25% above the cost price. If the article is sold by allowing 10% di

Brilliant_brown [7]

Answer: 13%

Step-by-step explanation:

Step 1:

5000

10% of 5000=500

5% of 5000=250

25%=500+500+250= 1250 rupees

so...

5000-1250= 3750 INR, which is the original price, <u>BEFORE THE 25% WAS ADDED</u>

but..

They only want a 10% discount of the price which is 25% above the cost (5000). So essentially we want to find 15%, because 25%-10%=15%

so if...

10%=500

5%=250

15%=750 INR

this means the price with the 10% discount off 25%= 4250 INR (5000-750)

now we need to find the percentage change. For this we need to subtract the price with the 15% discount with the price BEFORE THE 25% was added

e.g 4250-3750= 500INR

Then.. divide this price with the original price before the 25% was added

e.g 500/3750= 2/15=0.13

So...

Convert 0.13 into a percentage=13%

The PERCENTAGE PROFIT of the owner is 13%

P.S Please could someone double check this answer as I am only 15 years old and may have gotten some working out wrong! Thank you

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2 years ago

Jane's cat weighs 4.225 kilograms. How does the value represented by the 2 in the hundredths place compare with the value repres

denis-greek [22]

The two in the hundredths place is ten times less than the two in the tenths place.

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3 years ago

Read 2 more answers

Given a mean of 24.5 and a standard deviation of 1.7 what is the z score of the value 24 rounded to the nearest tenth?

Softa [21]

The correct answer is B) -0.3

Z-scores are found using the formula

z = (X-μ)/σ

For this problem, we have

z = (24-24.5)/1.7 = -0.5/1.7 = -0.3

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3 years ago