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Vinil7 [7]
2 years ago
6

A random variable X follows the uniform distribution with a lower limit of 670 and an upper limit of 750.a. Calculate the mean a

nd the standard deviation for the distribution. (Round intermediate calculation for standard deviation to 4 decimal places and final answer to 2 decimal places.)
Mathematics
1 answer:
DENIUS [597]2 years ago
8 0

You can compute both the mean and second moment directly using the density function; in this case, it's

f_X(x)=\begin{cases}\frac1{750-670}=\frac1{80}&\text{for }670\le x\le750\\0&\text{otherwise}\end{cases}

Then the mean (first moment) is

E[X]=\displaystyle\int_{-\infty}^\infty x\,f_X(x)\,\mathrm dx=\frac1{80}\int_{670}^{750}x\,\mathrm dx=710

and the second moment is

E[X^2]=\displaystyle\int_{-\infty}^\infty x^2\,f_X(x)\,\mathrm dx=\frac1{80}\int_{670}^{750}x^2\,\mathrm dx=\frac{1,513,900}3

The second moment is useful in finding the variance, which is given by

V[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2=\dfrac{1,513,900}3-710^2=\dfrac{1600}3

You get the standard deviation by taking the square root of the variance, and so

\sqrt{V[X]}=\sqrt{\dfrac{1600}3}\approx23.09

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To reverse a percentage decrease you divide it by the decrease (+ 100%)
For example we will pick the number, 100, which is decreased by 15% to 85.

To make 85 back to 100 we divide it by the decrease (1-0.15):
85 / 0.85 = 100

To find out how much 85 increased to get back to 100, we do:
15 / 85 = 0.1765 = %17.65

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Because percentages stay the same, this is applicable to any numbers, from this, we know that whenever something is reduced by 15% - when restored to it's original is increased by %17.65

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6 0
3 years ago
Don’t need help with the scatter plot really I just need help finding the Correlation coefficient
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5 0
2 years ago
Which expression gives the same result as shown problem?
sineoko [7]
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5\sum\limits_{i=0}^{4}{\left(\dfrac{1}{3}\right)^{i}}
8 0
3 years ago
sophie was 28 years old when daughter Nichole was born. In how many years will Sophie be two years less than still times Nichole
Kamila [148]
It will take 6 years for that to happen. 

You can find this by setting Nichole's age as x and Sophie's age as x + 28 since she will always be 28 years older. 

Now we are looking for a time that Sophie's age is equal to 2 less than 6 times Nichole's age. So we can set up the below equation. 

6(x) - 2 = x + 28
6x - 2 = x + 28
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This let's us know that it needs to be when Nichole is 6, which is 6 years in the future. 
6 0
3 years ago
Write each number without exponent 6.453 x 10^-3
Solnce55 [7]

Answer:

.006453

Step-by-step explanation:

6.453 x 10^-3

Move the decimal 3 places to the left since the exponent is negative

006.453

.006453

7 0
2 years ago
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