Write the number three million seven hundred thousand

HURRY!! WHOEVER ANSWERS FIRST WILL BE THE BRAINLIEST!!

beks73 [17]

These answers are all the same equation :/ they are all right, they all go right through the point :/

4 0

4 years ago

Exercise 5.2. Suppose that X has moment generating function

soldi70 [24.7K]

Answer:

a) Mean, E(X) = - 0.5

Variance = = 9.25

b) $M_{X}(t)=E(e^{tX})$

or

⇒ $=\sum e^{tx}p(x)$

⇒ $=\frac{1}{2}+\frac{1}{3}e^{-4t}+\frac{1}{6}e^{5t}$

Step-by-step explanation:

Given:

moment generating function of X as:

MX(t) = $\frac{1}{2} + \frac{1}{3}e^{-4t} + \frac{1}{6} e^{5t}$

a) Now

Mean, E(X) = $M_{X}'(t=0)$

Thus,

$M_{X}'(t)=\frac{1}{3}(-4)e^{-4t}+\frac{1}{6}(5)e^{5t}$

or

$M_{X}'(t)=\frac{-4}{3}e^{-4t}+\frac{5}{6}e^{5t}$

also,

$E(X^{2})=M_{X}''(t=0)$

Thus,

$M_{X}''(t)=\frac{-4}{3}(-4)e^{-4t}+\frac{5}{6}(5)e^{5t}$

or

$M_{X}''(t)=\frac{16}{3}e^{-4t}+\frac{25}{6}e^{5t}$

Therefore,

Mean, E(X) = $M_{X}'(t=0)=\frac{-4}{3}e^{-4(0)}+\frac{5}{6}e^{5(0)}$

or

Mean, E(X) = - 0.5

and

$E(X^{2})=M_{X}''(t=0)=\frac{16}{3}e^{-4(0)}+\frac{25}{6}e^{5(0)}$

or

$E(X^{2})$ = 9.5

also,

Variance(X) = E(X²) - E(X)²

⇒ 9.5 - (-0.5)²

= 9.25

b) Now,

Let f(x) be the PMF of X

Thus,

$M_{X}(t)=E(e^{tX})$

or

⇒ $=\sum e^{tx}p(x)$

⇒ $=\frac{1}{2}+\frac{1}{3}e^{-4t}+\frac{1}{6}e^{5t}$

Therefore,

at x = 0, P(x) = $\frac{1}{2}$

at x= - 4 ,P(x) = $\frac{1}{3}$

at x = 5, P(x) = $\frac{1}{6}$

Thus,

E(X) = $\sum xP(x)=0(\frac{1}{2})+(-4)(\frac{1}{3})+5(\frac{1}{6})$

or

E(X) = - 0.5

also, $E(X^{2})=\sum x^{2}P(x)=0^{2}(\frac{1}{2})+(-4)^{2}(\frac{1}{3})+5^{2}(\frac{1}{6})$

$E(X^{2})$ = 9.5

Hence,

Var(X) = E(X²) - E(X)²

⇒ 9.5 - (-0.5)²

= 9.25

4 0

4 years ago

A sample of marble has a volume of 6 cm3 and a density of 2.76 g/cm3. What is its mass?

Alenkasestr [34]

To solve for the mass of a substance is to simply get the product of volume and density, that is:

mass = density * volume

So calculating for mass:

mass = (2.76 g / cm^3) * 6 cm^3

3 0

3 years ago

Read 2 more answers

Find the volume of the following solid:

goblinko [34]

Answer:

93214.28 cm³

Step-by-step explanation:

The area of the given solid in the front side is = area of the rectangle + area of the semi circle.

= ( 40 × 30 ) + 0.5 × π × r²

= $(40 \times 30) + 0.5 \times \frac{22}{7} \times 15^{2}$ {Since radius = 0.5 × Diameter = 0.5 × 30 = 15 cm}

= 1553.57 cm².

Now the volume of the solid is given by (Area of the vertical surface × horizontal length) = 1553.57 × 60 = 93214.28 cm³ (Answer)

5 0

3 years ago

The length of a towel is 75 cm. How long is the towel in inches. Round to the nearest hundredth, if necessary.

Mice21 [21]

Answer:

Below.

Step-by-step explanation:

Convert from cm to inch divide by 2.54. 75/2.54= 29.5276...

Rounded to: 29.53 inches.

7 0

2 years ago