What is the significance of understanding the probability density function of exponential distribution? The cumulative distribution function can be understood as the probability of ≤ that time. What about the probability density?

The function of exponential distribution is mainly to be used as an approximation of the distribution of various "lifetimes"
It is a normal phenomenon that the value of probability density function is greater than 1. As long as the integral of the density function is unique in the whole domain of definition, I think you have confused the density function with the distribution function. If you have any questions, you can continue to ask

What is the probability density function of n-dimensional normal distribution?

Multivariate means that the sample is described by multiple variables or has multiple attributes, which is generally represented by d-dimensional eigenvector, x = [x1 The normal distribution of the eigenvector of dimension, XD] T.D is expressed by the following formula
Where μ is the mean vector of X, which is also the D dimension,
　　μ＝E{X}＝[μ1,μ2,… ,μd]T (2-33)
Σ is the covariance matrix of D × D dimension, and Σ - 1 is the inverse matrix of Σ, and | Σ | is the determinant of Σ
　　Σ＝E{(X－μ)(X－μ)T} (2-34)
Σ is a nonnegative matrix. Here we only consider the positive definite matrix, that is | ∑| > 0
Do you want to write it down or what

In an, A1 = 3, an + an-1 + 2N-1 = 0 (n ∈ n *, and N ≥ 2). 1. Prove that an + n is an equal ratio sequence, and find the general formula of an
1. It is proved that the sequence an + n is an equal ratio sequence, and the general term formula of an is obtained. 2

(1) From the problem an + an-1 + 2N-1 = 0, we can get an + n = - (an-1 + n-1), so {an + n} forms an equal ratio sequence with the first term a1 + 1 = 4 and the common ratio - 1, so an + n = 4 (- 1) ^ (n-1) so an = 4 (- 1) ^ (n-1) - n (2). From an = 4 (- 1) ^ (n-1) - N and the summation formula, we can get Sn = 2-2 (- 1) ^ n - [n (n + 1)] / 2

Column equation calculation: the product of X and 4, plus the quotient of 20 divided by 160, and the sum is 120, find X
Solution equation: 7 * 9-8x = 7 350 / x = 840 / 12

4x+20/160=120
4x+1/8=120
Multiply both sides by eight at the same time
32x＋1＝960
32x＝959
x＝29.96875
7*9-8x=7
8x＝56
x＝7
350/x=840/12
840x＝350×12
x＝5

What is the story of mother-in-law's tattoo?

Song Marshal Zongze was seriously ill and handed over the seal letter to Yue Fei for custody. He died of vomiting blood. Du Chong was ordered to seal the letter on behalf of Yue Fei. He was not good at fighting against Jin Dynasty. Yue Fei was depressed and went home to visit his mother privately. His mother-in-law urged him to go back to camp to fight against the enemy, and stabbed the word "loyal to serve the country" on Yue Fei's back, so that he would serve his country forever

In order to know that a, B and C belong to positive real numbers, it is proved that the cube of a + the cube of B + the cube of C is greater than or equal to one third of (a + B + C) (a + B + C)
Urgent! The smart man came to answer for me,

100 * 5% + X * 5% / 100 + x = 25% to solve the equation

100*5%+X*5%/100+X=25%
5+0.0005X+X=0.25
1.0005X=0.25-5=-4.75
X=-4.75÷1.0005
X=-9500/2001

Calculation formula of cube area calculation formula of cube volume

Area = side length × side length × 6
Volume = side length × side length × side length

If Sina + 3cosa = 0, find sin (π + a) cos (π - a)

From Sina + 3cosa = 0, sina × Sina + 3cosa × Sina = 0; Sina × cosa + 3cosa × cosa = 0
That is, sin2a + 3cosa × cosa = 0; Sina × Sina + 3 / 2sin2a = 0 and Sina × Sina + Cosa × cosa = 1
So we can get sin2a = - 3 / 5
So sin (π + a) cos (π - a) = - sin a × cos (a) = - Sin 2A = 3 / 5

For example, 3 (x + y) - 4 (x - y) = 9 / 2 x + y + 6 / 6 x - y = 1 (2)
How to eliminate the denominator

Re expression of equation: (x + y) / 2 + (X-Y) / 6 = 1
How to eliminate the denominator!
Multiply both sides by the least common multiple 6 of 2 and 6 to get
3(x+y)+(x-y)=6
If it is not redundant, it is better to solve the binary linear equations about "x + Y" and "X-Y" first!

What is the significance of understanding the probability density function of exponential distribution? The cumulative distribution function can be understood as the probability of ≤ that time. What about the probability density?