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Paul [167]
2 years ago
11

Helpppppppppppppppppp​

Mathematics
1 answer:
Elodia [21]2 years ago
5 0

We can't see the container. You should ask again with a different picture so you can get the right answer.

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Let X ~ N(0, 1) and Y = eX. Y is called a log-normal random variable.
Cloud [144]

If F_Y(y) is the cumulative distribution function for Y, then

F_Y(y)=P(Y\le y)=P(e^X\le y)=P(X\le\ln y)=F_X(\ln y)

Then the probability density function for Y is f_Y(y)={F_Y}'(y):

f_Y(y)=\dfrac{\mathrm d}{\mathrm dy}F_X(\ln y)=\dfrac1yf_X(\ln y)=\begin{cases}\frac1{y\sqrt{2\pi}}e^{-\frac12(\ln y)^2}&\text{for }y>0\\0&\text{otherwise}\end{cases}

The nth moment of Y is

E[Y^n]=\displaystyle\int_{-\infty}^\infty y^nf_Y(y)\,\mathrm dy=\frac1{\sqrt{2\pi}}\int_0^\infty y^{n-1}e^{-\frac12(\ln y)^2}\,\mathrm dy

Let u=\ln y, so that \mathrm du=\frac{\mathrm dy}y and y^n=e^{nu}:

E[Y^n]=\displaystyle\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{nu}e^{-\frac12u^2}\,\mathrm du=\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{nu-\frac12u^2}\,\mathrm du

Complete the square in the exponent:

nu-\dfrac12u^2=-\dfrac12(u^2-2nu+n^2-n^2)=\dfrac12n^2-\dfrac12(u-n)^2

E[Y^n]=\displaystyle\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{\frac12(n^2-(u-n)^2)}\,\mathrm du=\frac{e^{\frac12n^2}}{\sqrt{2\pi}}\int_{-\infty}^\infty e^{-\frac12(u-n)^2}\,\mathrm du

But \frac1{\sqrt{2\pi}}e^{-\frac12(u-n)^2} is exactly the PDF of a normal distribution with mean n and variance 1; in other words, the 0th moment of a random variable U\sim N(n,1):

E[U^0]=\displaystyle\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{-\frac12(u-n)^2}\,\mathrm du=1

so we end up with

E[Y^n]=e^{\frac12n^2}

3 0
3 years ago
What is the sale price for your purchase if you have a 20% off coupon and you buy a shirt for $19.99 and pants for $10.
Andrew [12]
Answer: I believe it is $23.99

Explanation:
19.99+10= 29.99
29.99x0.2= 5.992
29.99-5.99= $23.99

I hope this helped!
4 0
3 years ago
Does anybody know the correct answer to this?
olganol [36]

Answer:

  • sin(X) = 4/5
  • cos(X) = 3/5
  • tan(X) = 4/3

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to help you remember the relations between sides and trig functions in a right triangle.

  Sin(X) = Opposite/Hypotenuse = 24/30 = 4/5

  Cos(X) = Adjacent/Hypotenuse = 18/30 = 3/5

  Tan(X) = Opposite/Adjacent = 24/18 = 4/3

_____

You may be expected to leave the trig ratios in the original unreduced form.

4 0
2 years ago
Math Sequence help!!
julia-pushkina [17]
Hello here is a solution :

6 0
3 years ago
3<br> Describe and correct the error a student made when graphing the linear equation y = -3/4x -6
likoan [24]

Answer:

In step 1 the y-intercept should be plotted at (0,-6)

Step-by-step explanation:

Remember that to find the Y intercept in any linear equation you need to use 0 as your X value, this means taking the formula in the y=mx+b form and replacing X with a 0.

Since the formula is y = -3/4x -6

We just insert a 0 insted of the "x"

y = -3/4(0) -6

y=0-6

y=6

So the y-intercept sould be placed in (0,-6)

That's what he did wrong when graphing the equation.

5 0
3 years ago
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