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yKpoI14uk [10]
3 years ago
5

A quantity x has cumulative distribution function p(x) = x − x2/4 for 0 ≤ x ≤ 2 and p(x) = 0 for x < 0 and p(x) = 1 for x &gt

; 2. find the mean and median of x.
Mathematics
1 answer:
34kurt3 years ago
3 0
F_X(x)=\begin{cases}0&\text{for }x2\end{cases}

Recall that the PDF is given by the derivative of the CDF:

f_X(x)=\dfrac{\mathrm dF_X(x)}{\mathrm dx}=\begin{cases}1-\dfrac x2\\\\0&\text{otherwise}\end{cases}

The mean is given by

\mathbb E[X]=\displaystyle\int_{-\infty}^\infty x\,f_X(x)\,\mathrm dx=\int_0^2\left(x-\dfrac{x^2}2\right)\,\mathrm dx=\frac23

The median is the number M such that F_X(x)=\mathbb P(X\le M)=\dfrac12. We have

F_X(M)=M-\dfrac{M^2}4=\dfrac12\implies M=2\pm\sqrt2

but both roots can't be medians. As a matter of fact, the median must satisfy 0\le M\le2, so we take the solution with the negative root. So M=2-\sqrt2 is the median.
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What is 7/9, 13/18, 5/6, and 2/3 in least to greatest order?
Vlad [161]

Answer:

2/3 , 13/18, 7/9 , 5/6 (least to greatest order)


Step-by-step explanation:

1.  You need to convert all the fractions into decimal form .

2. 7/9.00 = 0.78 (rounded)

3. 13/18.00 = 0.72

4. 5/6.00 = 0.83

5 . 2/3.00= 0.67 (rounded)


7 0
3 years ago
$500 are deposited into an account semiannuallysemiannually  for six years at an interest rate of 7.2​% compounded semiannually.
kobusy [5.1K]
Each year 107.2%increase of budget
first year 500 * 1.072 = 536
second year 536 * 1.072 = 574.592
third year 574.592 * 1.072 = 615.962624
..
..
sixth year 707.854392 *  1.072 = 758.819908

or you can just (1.072)^6 * 500 = 1.517639816659862 * 500 = 758.8199083299308

bingo........

8 0
2 years ago
Read 2 more answers
Drag each number to the correct location on the table.
ASHA 777 [7]

Answer:

\text{Rational number} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{ Irrational number}

          3\sqrt{25}  \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sqrt{141}\\\\\sqrt{256} \\\\1. \overline{ 1625} \\\\\frac{-11}{151}

Step-by-step explanation:

Since we believe it  

The number sequence is that those which can be described as \frac{p}{q} and that is not ending and recurring.  Figures that are unreasonable are also the ones, that are not \frac{p}{q} and therefore are non-ending, non-recurring.  

The number sequence is 3\sqrt{25} = 3 \times 5 = 15

Rational amount since it is classified as \frac{p}{q}  .\frac{-11}{151} is really a rational number.  

1.\overline{1.625} is a real function, since it does not end but repeats it.  

The rational number \sqrt {256} = 16

Unreasonable number \sqrt{141}.

7 0
3 years ago
Read 2 more answers
What is the equation of the line that passes through point(7, -8) and has a slope of zero? A. y =7B. x = 7C. x = -8D. y = -8
Bond [772]

y = -8

y = mx + b, where m is the slope and b is the y intercept

since m = 0, the term mx = 0

since the line passes throug (7, -8) then y = -8

6 0
9 months ago
In 2015 han was paid £1350 per month what was his average pay per hour in 2016
ASHA 777 [7]

His average pay was:

Answer:

£1350

----------- = £8.44/hr   based upon  160 work hours per week

160 hr

Step-by-step explanation:

We must assume that Han works a standard 40-hour week, and that there are 4 weeks in each month.  That comes to 160 hours.

Then his average hourly pay rate was

£1350

--------- = £8.44

160 hr

3 0
3 years ago
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