Find the numbers whose difference is five and whose product is 266

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

Find the length of BC, in simplest radical form.

zubka84 [21]

9514 1404 393

Answer:

BC = 16 +12√3

Step-by-step explanation:

In the attached, we see that ∆ABE is a 30°-60°-90° triangle with AB the short side and BE the hypotenuse. Then BE = 2·AB = 12√3.

EC is the side opposite AD in parallelogram ADCE, so is the same length, 16.

The length BC is ...

BC = EC +BE

BC = 16 +12√3

8 0

3 years ago

It takes Maya 30 minutes to solve 5 logic puzzles. At this rate, how many logic puzzles does she solve in 1 hour 30 minutes?

denis23 [38]

30 minutes = 5 puzzles

60 minutes = 10 puzzles

90 minutes = 15 puzzles

She will solve 15 puzzles in an hour and 30 minutes

4 0

3 years ago

Read 2 more answers

Please help me with both questions whoever does the best I will mark brainlest.

DochEvi [55]

A function assigns the values. The force that will be required to move the rock is 48 lbs.

<h3>What is a Function?</h3>

A function assigns the value of each element of one set to the other specific element of another set.

A.) The inverse of the function f(x)=1/x is,

f(x) = 1/x

y = 1/x

x = 1/y

g(x)=1/x

Hence, The inverse of the function f(x)=1/x is g(x)=1/x.

B.) The force that will be required to move the rock using the momentum,

9ft × 80lbs = 15 ft × F

F = 48 lbs

Hence, The force that will be required to move the rock is 48 lbs.

Learn more about Function:

brainly.com/question/5245372

#SPJ1

8 0

2 years ago

What is 2.161616 as a fraction?

Komok [63]

repeating fraction, nice

2.16161616...=2+0.16161616...
solve the repeating part
let's say x=0.16161616
2 places repeat, multiply x by 10^2 or 100
100x=16.161616

now subtract x from taht
100x-x=16.161616-0.16161616
the repeats cancel and we get
99x=16
divide both sides b 99
x=16/99

so
16/99=0.16161616...

2+16/99 is the fraction
if ya wanted 1 fraction then
2+16/99=
198/99+16/99=
214/99

2.161616=214/99

8 0

3 years ago