Let the distribution density function of random variable X be p (x) = 1 / 2E ^ (- |e |) to find e (x)

Let the distribution density function of random variable X be p (x) = 1 / 2E ^ (- |e |) to find e (x)

I can't understand this question. Is x in the absolute value?
Which of the following expressions?
p（X）=(1/2)*e^(-|x|）
p（X）=1/[2e^(-|x|)]
In addition, does x have a value range?

Let the density function of random variable X be f (x) = the - K ^ 2x ^ 2 power of CXE, x > = 0, 0, X

Your expression is: F (x) = CXE ^ [- (k ^ 2) (x2)], K, C are constants, right
First of all, this is to calculate the expected integral in this form:
A=∫[(0,+∞),e^(-x^2)]dx,
Let's first calculate: A ^ 2 = ∫ [(0, + ∞), e ^ (- x ^ 2)] DX ∫ [(0, + ∞), e ^ (- y ^ 2)] dy
=∫[(0,+∞)]dx∫[(0,+∞),e^(-x^2-y^2)dy
In the above formula, we can change to the following: x = RCOs θ, y = rsin θ
A^2=∫[(0,π/2)]dθ∫[(0,+∞),re^(-r^2)]dr=π/4
So a = (√π) / 2,
You should know it next

Let the random variable x obey the exponential distribution of parameter λ = 1, and find the density function of the random variable y = e ^ X

fx(x)=e^-x,(x>=0)
So FY (y) = P (y = e ^ x)

Let the random variable x obey the exponential distribution with input = 1, and find the density function of the random variable y = x2

Y=X^2>0
When py (y) = {0, Y0, FY (y) = P (- y ^ (1 / 2)

What is the significance of the study of distribution function to probability theory and mathematical statistics

Probability theory research project has the distribution function, the distribution function is very important, the mathematical statistics basic does not use the distribution function, mainly is to each kind of function distribution research

The radius of the cone bottom is r, and the cross section of the axis is a right triangle

The shaft section should be composed of two generatrix and the diameter of the bottom surface to form a right triangle According to the fact that the sectional area is equal to the square of the generatrix times the arc length of the expanded sector divided by two, the arc length is equal to the circumference of the bottom circle Because some symbols are not easy to play, let's solve them here!

How to understand that the distribution function f (x) is right continuous in probability theory and mathematical statistics?

The real point must be at the right end
For example, there is a breakpoint somewhere, such as x = 0
f(x)
=0 x=0
This is the right continuous, the right part of the partition interval with an equal sign

I want to know that there are several forms of conic intersection. Please answer carefully and tell me why,

Circle, parabola, hyperbola, ellipse
Because it's all a curve system
You can see the picture from the cover of the chapter in the math book

Let the distribution function f (x) of random variable X be continuous, and find the probability density function of random variable f (x)!
But I don't understand,
Let y = f (x)
When y

Because y ~ f (x)
F (x) is a distribution function with a range of 0 ~ 1
So the random variable y should also take the number between 0 and 1
When y

If the plane π is parallel to the axis of the cone and the angle between the generatrix of the cone and the axis is 60 degrees, then the eccentricity of the intersection of the plane and the cone is 0

Option 2
Let the angle between the plane and the axis be β
The angle between the generatrix and the axis is α
Cos β = 2
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