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Vinil7 [7]
3 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]3 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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4 0
3 years ago
The sum of two consecutive integers is 201 find the integers
telo118 [61]

100 and 101

the two integers are n and n+1. this means that 2n+1=201. n=100 and n+1=101

8 0
2 years ago
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1+secA/sec A = sin^2 A / 1-cos A​
Fofino [41]

Answer:  see proof below

<u>Step-by-step explanation:</u>

\dfrac{1+\sec A}{\sec A}=\dfrac{\sin^2 A}{1-\cos A}

Use the following Identities:

sec Ф = 1/cos Ф

cos² Ф + sin² Ф = 1

<u>Proof LHS → RHS</u>

\text{LHS:}\qquad \qquad \dfrac{1+\sec A}{\sec A}

\text{Identity:}\qquad \qquad \dfrac{1+\frac{1}{\cos A}}{\frac{1}{\cos A}}

\text{Simplify:}\qquad \qquad \dfrac{\frac{\cos A+1}{\cos A}}{\frac{1}{\cos A}}\\\\\\.\qquad \qquad \qquad =\dfrac{1+\cos A}{1}

\text{Multiply:}\qquad \qquad \dfrac{1+\cos A}{1}\cdot \bigg(\dfrac{1-\cos A}{1-\cos A}\bigg)\\\\\\.\qquad \qquad \qquad =\dfrac{1-\cos^2 A}{1-\cos A}

\text{Identity:}\qquad \qquad \dfrac{\sin^2 A}{1-\cos A}

\text{LHS = RHS:}\quad \dfrac{\sin^2 A}{1-\cos A}=\dfrac{\sin^2 A}{1-\cos A}\quad \checkmark

3 0
3 years ago
A square park is 75 m long. Find the area of the park.<br>​
Inga [223]
5625 m^2

If is is square, all sides must be congruent (all sides are 75m). To find area, you multiply width x length (how long). Therefore:

75m x 75m = 5626 m^2
3 0
3 years ago
Which of the following numbers is not a perfect square?<br><br> 24<br> 25<br> 64<br> 100
stich3 [128]
Hi! 

A perfect square is the product of when a whole number is multiplied by itself

Ex:

6 × 6 = 36, 36 is the perfect square. 

The number that is being multiplied is the square root. 

So to find the correct answer for this question, let's use the process of elimination. 

100 = 10 × 10 so we can cross out 100

64 = 8 × 8 so we can cross out 64

25 = 5 × 5 so we can cross out 25

Now all we have left is 24, which is not a perfect square. 

Answer: A. 24

Hope this helps :)
8 0
3 years ago
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