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Why is a zero probability event not necessarily impossible
For continuous random variables, such as a drop of water from the basin, the probability of a drop of water being taken is 1 / N, n tends to infinity, so the probability is zero
Probability theory says that the probability of an impossible event is zero, but a zero probability event can happen. For example, if you take a person in the universe, you can get your probability. This is an example of a zero probability event that can happen!
Random variables are divided into continuous and discrete, and their distribution descriptions are different
For continuous random variables, the probability density value of a specific point is a bounded constant, which can be arbitrary (including 0 and 1). But because the point has no length, the probability density integral of the point is 0 (because the probability density value of the point is bounded), that is, the probability of the event corresponding to the point is 0, but the event is still possible, Similarly, the probability density of a point is 1, but the probability density integral of the point is still 0, so the event with probability 1 does not necessarily occur. In short, for continuous random variables, it is meaningless to discuss the probability of a single point (all are 0), The probability that the random variable falls into an interval
For a discrete random variable, if its event domain is finite, it can be considered that the event with a probability of 0 will not happen, and the event with a probability of 1 will happen. But if the event is infinite, it needs to be analyzed concretely
Since all events with zero probability are possible, events with a probability approaching zero are indeed possible. However, when we deal with problems, we usually count events with a probability approaching zero as events with zero probability, which is not absolute
If x2 + (m-2) x + 9 is a complete square, then the value of M is______ ．
∵ x2 + (m-2) x + 9 is a complete square form, ∵ x2 + (m-2) x + 9 = (x ± 3) 2, and (x ± 3) 2 ∵ x2 ± 6x + 9, ∵ m-2 = ± 6, ∵ M = 8 or M = - 4
If x2 + 2mx + 9 is a complete square, then M=______ ．
∵ x2 + 2mx + 9 is a complete square form, ∵ x2 + 2mx + 9 = (x ± 3) 2 = x2 ± 6x + 9, ∵ 2m = ± 6, M = ± 3
Please write a mixed operation problem of one to rational number and solve it. The problem should meet the following conditions at the same time
1. It must contain the power of addition, subtraction, multiplication and division 2. The divisor must be negative 3. The calculation result is equal to 2012
Square of 2 × [(- 1000) / (- 2) + 3]
=Square of 2 × [500 + 3]
=4*503
=2012
How to deduce the formula of the instantaneous velocity of the midpoint of the displacement of the uniform linear motion
The specific formula is VN = [xn + X (n + 1)] / 2T (generally used in the experimental problem of speed measurement by dot timer). This formula is hard to come up with~
What I want is not the formula of V = root ((V0 ^ 2 + VT ^ 2) / 2), but the formula of displacement above!
V(n-1)=Xn/T
V(n+1)=X(n+1)/T
Vn=[V(n-1)+V(n+1)]/2
=[Xn+X(n+1)]/2T
1. If the number of a increases by 25% and is equal to the number of B, what percentage of the original number of a is that of B?
2. Form a formula with five 3's, and the results are 0,1,2,3 respectively
1.1÷（1+25%）=80%
2.3+3-3+3-3=3
3-3÷3-3÷3=1
3-3+3-3÷3=2
(3-3）×3×3×3=0
Derivation of the relationship between the instantaneous velocity in the middle of a section of displacement and the initial and final velocity of this section of displacement
How to get V (s / 2) ^ 2-v0 ^ 2 = 2A * s / 2 from vt ^ 2-v0 ^ 2 = 2As in the derivation process of V = root sign (VT ^ 2 + V0 ^ 2) / 2
Uniform speed change
In VT ^ 2-V ^ 2 = 2As
In V ^ 2-VO ^ 2 = 2As (total displacement 2S)
therefore
Vt ^ 2-V middle ^ 2 = V middle ^ 2-VO ^ 2
In 2V ^ 2 = VT ^ 2 + VO ^ 2
V middle = √ [(VT ^ 2 + VO ^ 2) / 2]
Fifth grade next semester mathematics formulaic calculation question, has how many writes how many
1.3/7 × 49/9 - 4/3 2.8/9 × 15/36 + 1/27 3.12× 5/6 – 2/9 ×3 4.8× 5/4 + 1/4 5.6÷ 3/8 – 3/8 ÷6 6.4/7 × 5/9 + 3/7 × 5/9 7.5/2 -（ 3/2 + 4/5 ） 8.7/8 + （ 1/8 + 1/9 ） 9.9 × 5/6 + 5/6 10.3/4 ×...
The formula of median velocity of uniform acceleration motion is deduced
How to deduce the median velocity = root ((V0 ^ 2 + VT ^ 2) / 2)? Note: it is not the median velocity
Vt ^ 2-v0 ^ 2 = 2As VT ^ 2-vm ^ 2 = 2A * s / 2 = as VM ^ 2-v0 ^ 2 = 2A * s / 2 = as
Vt ^ 2-vm ^ 2 = VM ^ 2-v0 ^ 2, so VM = root ((V0 ^ 2 + VT ^ 2) / 2)
Sixth grade mathematics application problem (how to do? Urgent, fast!)
There are 60 tons of cement in a construction site, 1 / 4 of which is used in the first day, and 9 / 2 in the second day. How many tons of cement are still on the construction site?
60 * (1-1 / 4) - 9 / 2 = 81 / 2 = 40.5 tons
RELATED INFORMATIONS
- 1. It is known that the quadratic trinomial x2-2 (M + 1) x + 9 is a complete square, then M=______ ．
- 2. Expression of power function f (x) passing through point m (3, √ 3)
- 3. Given the function g (x) = 1 + 2x, f [g (x)] = 1 + x2 / X2, find the expression of F (x)
- 4. Can a in all trigonometric functions of the form y = asin (Wx + F) + B be represented by (ymax Ymin) / 2, or is it necessary for y to be symmetric about the X axis?
- 5. It is known that the period of the function f (x) = asinwx + bcoswx + 1 defined on R is π, F (π / 4) = root 3 + 1, and the maximum value of F (x) is 3 1. Write the f (x) expression 2. Write down the center of the pile, the axis of symmetry, and the axis 3. Explain how the image of F (x) is transformed from the image of function y = 2sin2x
- 6. How to find the period according to the harmonic motion image The vertical axis is amplitude and the horizontal axis is time
- 7. If two function images are symmetric about the Y axis, then what is their relationship
- 8. A problem of linear function It is known that the coordinates of three points a, B and C in the rectangular coordinate system are (3,3) (- 6, m) (n, - 2), respectively. The three points are in the first three or four quadrants, and the line where AB is located passes through the origin o (1) Find the function analytic formula of AB and the value of M; (2) If part of the triangle of △ ABC in the first quadrant is folded along the x-axis, point a just falls on the side of BC 1. Find the function analytic formula of the line where BC is located and the point C coordinate; 2. If P is a point on the x-axis, the triangle with vertices o, C and P is an isosceles triangle
- 9. If y = - 2Sin (x + φ) (0
- 10. It is known that the minimum period of function f (x) = asin (2 ω x + π / 6) + A / 2 + B (x ∈ R, a ＞ 0, ω ＞ 0) is π, and the maximum value of function f (x) is 7 / 4 It is known that the minimum period of function f (x) = asin (2 ω x + π / 6) + A / 2 + B (x ∈ R, a > 0, ω > 0) is π, and the maximum value of function f (x) is 7 / 4, The minimum value is 3 / 4 (1) find the value of a B ω (2) point out the monotone increasing interval of F (x) (3) point out the set of X when f (x) gets the maximum and minimum value
- 11. Probability of independent events A. B is two random events, P (a) = 0.5, P (b) = 0.3, if a and B are independent Then p (AUB) =?
- 12. It is easy to give an example that the event with probability 0 is not an impossible event, and the event with probability 1 is not an inevitable event It's better to be more detailed
- 13. An event with probability equal to one is not necessarily an inevitable event, and an event with probability equal to zero is not necessarily an impossible event
- 14. There are three red, black and white balls in box a, and two yellow, black and white balls in box B. take one ball from each box. Calculate the probability that the two balls are of different colors
- 15. There are 10 students in a group, including 3 girls. Two representatives are elected. The probability of at least one girl being elected is () A. 715B. 815C. 35D. 25
- 16. Take any two balls from the pocket with two red balls and two white balls. In the following groups, the two events are mutually exclusive and not antagonistic______ (please write down all the serial numbers you think meet the requirements) ① at least one white ball; all white balls; ② at least one white ball; at most one white ball; ③ exactly one white ball; exactly two white balls; ④ at least one white ball; all red balls
- 17. There is a probability problem of the occurrence of mutually exclusive events in mathematics A cube with color on each side is sawed into N3 cubes (n is greater than or equal to 3) of the same size, and the probability of any one of these cubes with color on exactly two sides is zero The correct answer is 1 - (n-2) 3 / N3, and the main explanation is (n-2) 3 Sorry, I copied the wrong topic, at least one side of the probability of color
- 18. There are two coats in Xiao Wang's wardrobe, one is red, the other is yellow, and there are three pairs of trousers, which are white, blue and yellow. If you take out a coat and a pair of trousers at will, the probability is () A. 56B. 16C. 13D. 15
- 19. In medical biological experiments, Drosophila melanogaster is often used as the test object. In a cage with 6 Drosophila melanogaster, two flies are accidentally mixed into the cage (at this time, there are 8 flies in the cage: 6 Drosophila melanogaster and 2 flies), so we have to open a small hole in the cage, let the flies fly out one by one, until both flies fly out, and then close the hole. (I) just one Drosophila melanogaster is left in the cage (II) the probability of at least five flies remaining in the cage
- 20. In the 2013 National University Games, a University selected 4 students from 6 students to participate in shot put, height adjustment, long jump and sprint respectively, then the probability of student a to participate in sprint or long jump is () A. 13B. 12C. 23D. 34