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3 years ago

Suppose () = 1/8 for 0 ≤ ≤ 4 for x being a continuous random variable Is () a probability density function? Prove or disprove.

Mathematics

1 answer:

matrenka [14]3 years ago

4 0

Answer:

The expected value of x ; E(x) = 1

Step-by-step explanation:

F(x) = 1/8 for 0 ≤ x ≤ 4

To prove that it is a probability density function we will find E(x )

attached below is the required prove

It is proven that F(x) = 1/8 for 0 ≤ x ≤ 4 is probability density function

The expected value of X = 1

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Mice21 [21]

Total cost = a + (13a/100)

Step-by-step explanation:

Let the price of the monster truck be 'a'

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The equation to represent the total cost is

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3 years ago

Determine whether The given segments have the same length. Justify your answer

Semenov [28]

We know the distance formula is

$\sqrt{ (x_{2}-x_{1})^2+ (y_{2}-y_{1})^2 }$

Here A( -4,2) and B(1,4)

So length of AB

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Also C(2,1)

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= $\sqrt{(2-1)^2+(-1-4)^2} =\sqrt{1^2+(-5)^2} =\sqrt{26}$

So we can see that length of AB is not equal to length of BC

11.

Now AB = $\sqrt{29}$

Also C(2,-1) & D(4,4)

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3 years ago

Is (x+5) a factor of f(x)=x^3 - 4x^2 + 3x + 7? use either the remainder theorem or the factor theorem to explain your reasoning.

Rufina [12.5K]

Answer:

Step-by-step explanation:

Use synthetic division

-5 | 1 -4 3 7

____-5 45 -240

1 -9 48 | -233

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2 years ago

<img src="https://tex.z-dn.net/?f=%20%5Crm%20%5Cint_%7B0%7D%5E2%20%5Cleft%28%20%5Csqrt%5B3%5D%7B%20%7Bx%7D%5E%7B2%7D%20%20%2B%20

Verizon [17]

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$\displaystyle \int_a^b f(x) \, dx = b f(b) - a f(a) - \int_{f(a)}^{f(b)} f^{-1}(x) \, dx$

Let $f(x) = \sqrt{1 + x^3}$ . Compute the inverse:

$f\left(f^{-1}(x)\right) = \sqrt{1 + f^{-1}(x)^3} = x \implies f^{-1}(x) = \sqrt[3]{x^2-1}$

and we immediately notice that $f^{-1}(x+1)=\sqrt[3]{x^2+2x}$ .

So, we can write the given integral as

$\displaystyle \int_0^2 f^{-1}(x+1) + f(x) \, dx$

Splitting up terms and replacing $x \to x-1$ in the first integral, we get

$\displaystyle \int_1^3 f^{-1}(x) \, dx + \int_0^2 f(x) \, dx = 2 f(2) - 0 f(0) = 2\times3+0\times1=\boxed{6}$

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1 year ago

What is the width of a rectangle with an area of 5/8in2 and a length of 10 inches

Tju [1.3M]

A=lw

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w=1/16

Hope this helps :)

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3 years ago