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It is known that the density function of random variable x is f (x) = x, 0
F(x) = 1/2,0
Suppose x is a continuous random variable and the density function is f (x) = C / (1 + x ^ 2), then C =?
The global integral of density function is 1
∫(-∞,+∞)f(x)dx=c*arctanx|(-∞,+∞)=cπ=1
So C = 1 / π
If you have any suggestions, you are welcome to discuss and learn together,
Given that two random variables X and y are independent of each other and obey the uniform distribution on 0,1, the joint density function of X-Y and X is obtained
Let z = X-Y
When x = x,
Z is uniformly distributed on (x-1, x)
Fz|x (z|x) = 1. Z belongs to (x-1, x), X belongs to (0,1)
Others are 0
F (Z, x) = FZ | x (Z | x) f (x) = 1, Z belongs to (x-1, x), X belongs to (0,1)
Others are 0
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How to calculate the coefficient a and probability density function according to the distribution function of continuous random variables
I want to know how to find out a = 1
If the distribution function of continuous random variable is continuous, then f (1-0) = f (1) = f (1 + 0) = 1, and f (1-0) = a, so a = 1
The section plane is perpendicular to the axis of the cylinder, and the shape of the section line is
A. A pair of parallel lines
B. Circle
C. Ellipse
B circle
Let the density function of continuous random variable x satisfy f (x) = f (- x), and f (x) is the distribution function of X, then p (| x | > 2004)=
2F(2004)-1
A cone is cut by a plane, and the plane is inclined to its axis
As shown in the picture
Let the probability density function of random variable X be f (x) and f (x), and f (x) = f (- x), then for any real number a, f (- a) = f (- x)_____
Let the probability density function of random variable X be f (x) and f (x), and f (x) = f (- x), then for any real number a, f (- a) = f (- x)_____
A. 1/2-f(a) B. 1/2+F(a) C. 2F(a)-1 D. 1-F(a)
F(-a)=∫(-∞,-a)f(x)dx=∫(a,+∞)f(-t)dt=∫(a,+∞)f(t)dt=1-∫(-∞,a)f(x)dx=1-F(a)
So choose D
If a cone is cut by a plane parallel to the bottom, and the ratio of the length of the upper and lower sections of the generatrix is 1:3, then the ratio of the bottom area of the small cone to that of the large cone is 1:3
Ratio of bus length = 1:3
Radius ratio = 1: (1 + 3) = 1:4
So:
The ratio of the bottom area of a small cone to that of a large cone
=1²：4²
=1：16
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Let the density function of the random variable X be f (x), f (- x) = f (x), and f (x) be the distribution function of X, then it has a positive effect on any real number a
&Why
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