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Calculus knowledge used in probability theory and mathematical statistics Please do me a favor and help me list the calculus formulas needed for continuous random variables, I'm afraid of trouble. I'll write two questions. Do me a favor and help me write out the problem-solving process. In order to avoid any discrepancy between your expression and my understanding, you'd better refer to my expression, Question: 1： Integral number up 1 and down 0, integral number up 2 and down 0,1 / 2, xdydx =? (there are two consecutive integral signs in this question, and the 1 / 2 is in front of xdydx. I'm afraid we may have misunderstandings, so I write so, forgive me) 2： Integral number up x down 0,8xydy =? For the above two questions, please write the formula and the problem-solving process. It's troublesome, Say it The one downstairs solving problem two (y) ²/ 2) How did you get out? X of the last answer ³ How did you get here?
∫xdx=x ²/ 2,∫ydy=y ²/ 2,∫1dy=y
2： Integral number up x down 0,8xydy
=8x (integral number up x down 0, YDY)
= 8x(y ²/ 2) (bring in upper limit x minus lower limit 0)
= 8x(x ²- 0 ²)/ two
= 4x ³
1： Integral number up 1 and down 0, integral number up 2 and down 0,1 / 2, xdydx
=(1 / 2) (upper 1 and lower 0, xdx) (upper 2 and lower 0, 1dy)
= (1/2)[(x ²/ 2) (bring in upper limit 1 minus lower limit 0)] [(y) bring in upper limit 2 minus lower limit 0]
= (1/2)[(1 ²- 0 ²)/ 2][2-0]
= 1/2
What are the parts of probability theory, mathematical statistics and calculus
Calculus is a basic subject of probability theory
To learn probability theory well, you need to master the following knowledge points:
Logical algebra, derivative, single integral, double integral,
Sometimes there are triple integrals,
The convolution formula and the summation of sequence are applied
If you have any comments, welcome to discuss and learn together; If it helps,
What chapters of calculus do you need to learn probability theory and mathematical statistics?
Classical probability requires knowledge of permutation and combination high volume 2
Discrete in probability distribution does not need basis
Continuous only needs simple integral solution and function derivation. It won't be difficult as long as the graph is drawn
All the solutions are definite integrals, and there are formulas that can be set
Find the first derivative of the function y = 2x to the power of X + 3 to the power of - 3
y=2x ³＋ 3^x-3 ³
y'=(2x ³＋ 3^x-3 ³)'
=(2x ³)'+ (3^x)'-(3 ³)'
=6x ²+ 3^x·ln3 -0
=6x ²+ 3^x·ln3
What is the limit of the factorial of N divided by (2n)? How to prove it?
J = N^N/(2N)!= N/(2N) N/(2N-1)N/(2N-2)...N/(N+1)(1/N!) < 1/N!
Because: LIM (n -- > ∞) 1 / N= 0
Therefore: LIM (n -- > ∞) J = 0
The limit of the factorial ratio of n to the nth power of n
Take logarithm and get
ln(n!)/n^n
The calculation is defined by definite integral
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