# bernoulli

1. ### bernoulli's law

The height of a funnel is 20cm if the upper diameter is 20cm and the lower diameter is 2cm find the pressure difference between two cross sectional areas if in every second 0.3L of water pass through the funnel? P.s I translate this question from Persian sorry if there is any grammatical...
2. ### Bernoulli's DE

I think the attached DE matches Bernoulli's DE. I solved it to some extent and I'm not able to substitute the initial conditions in the final solution, as it is leading to 1/0 Please check and let me know where I went wrong. Thanks a lot.
3. ### Probability

"A lecturer teaches Digital Communication to 30 of her students. However she doesn't know if her student grasp her lecture. The students have to raise their hands if they dont grasp the lecture. She gives dice to a student and asks him to roll it. She does it with every student in the class...
4. ### Problem with Bernoulli trials

I have the following problem: We conduct a series of indipendent Bernoulli trials with probability of success p for each trial and let N be the number of trials until the first success. Next we conduct N independent Bernoulli trials with probability of success q for each trial and let X be...
5. ### Confidence interval with Bernoulli distribution

Hello, With have interval (0.45,0.55) and alpha = 0.88 How can calculate 'n' through Bernoulli distribution ? Thanks
6. ### Bernoulli function

Hi, I am trying to understand an example in the book, and I don't quite understand the following; please could someone explain further? Let X1,X2,X3, Xn be i.i.d Bernoulli r.v.s with parameter Î¸ such that Î¸ Ïµ (0,1) i.e. for i = 1,...,n, P(Xi = 1) = Î¸ P(Xi = 0) = 1- Î¸ We may write...
7. ### Bernoulli's Thereom

I am trying to locate the formula to calculate pressure (psi) when given pipe diameter and the velocity. This is a plumbing related question. I was using the formula v1p1= v2p2 and the answers are not correct. I uploaded the picture in the replies. Thanks in advance
8. ### Riccati Equation to Bernoulli to Linear

I was working the attached problem which asked that one demonstrate that a Riccati equation was reducible to a Bernoulli with the given substitution and then to bring that down to a linear equation. Can someone please explain why the signs change from the 2nd to last to the last step? Thank you...
9. ### Bernoulli Trials

I was just wondering if anyone could give me feed back on the following problem. In the exercise, X is a binomial variable with n = 5 and p = 0.1. Compute the given probability. (Round your answer to five decimal places.) n=5, p=0.1, q=0.9 P(X â‰¤ 4) So far I have...
10. ### bernoulli effect

I a having trouble understanding Bernoulli effect.... So as for example a fluid flowing through, pipe. The pipe becomes narrower. The water has to speed up because the pipe is rigid and does not stretch at all, so the same volume of water must be pushed along? ?? The same rate of volume must...
11. ### Bernoulli Trials

Hey, I'm new here (and new to math in general, more on that in a bit,) so I hope this is the correct area. So I've been reading this book. http://i.imgur.com/n37UZ4Y.jpg The reason for this is because throughout my years in high school, I've never truly paid attention to mathematics. By that I...
12. ### property of Bernoulli random variables

Let b_i, i=1, \ldots, n be Bernoulli random variables with probability P(b_i=1)=2k/n,where k\leq n.Show the following: Let \chibe an indicator function that kout of nofb_i are 1. Then, P(\chi=1)>1/2. Thank you.
13. ### estimation of a moment for the sum with Bernoulli random var

Let x be vector in R^n and let y_i, i=1, \ldots n be 0,1 Bernoulli random variables such that P(y_i=1)=m/n. Let p\geq 2 Estimate from above E(\left|\sum_{i=1}^nx_iy_i\right|^p)^{1/p}
14. ### Bernoulli inequality

Let d\in \mathbb{R} satisfy d>1. Use Bernoulli's inequality and by the definition of a limit to show that the sequence (d^n) is not bounded in \mathbb{R}, hence not convergent. My attempt: Let d = \frac{1}{1+a} where a>0. We know from Bernoulli's inequality that (1+a)^n\ge (1+na) hence...

17. ### Bernoulli equation

Hi, In fact, I always face a problem in solving these equations. Please take a look at this equation and my working: I hope that someone will show me their step-by-step work.
18. ### Bernoulli / Riccati Equation

Hello, I have an equation of the following form: y'(t) + Ay(t) + By(t)^m + c = 0 1/ With c=0, the equation is of the Bernoulli form, and might be integrated. 2/ With m = 2, it is a Riccati equation, which might be turn back to a Bernoulli one and then integrated 3/ My question is about the...
19. ### Bernoulli trials

Independent trials that result in a success with probability p and a failure with probability 1?p are called Bernoulli trials. Let Pn denote the probability that nBernoulli trials result in an even number of successes (0 being considered an even number). Given that: P_n = p(1 - P_{n-1}) +...
20. ### Bernoulli Polynomial

Define the Bernoulli Polynomials by P_0(x) = 1,\; for n\geq 1\,:\;\; P'_n(x) = nP_{n-1}(x),\; {\int_{0}}^{1} P_n(x)dx = 0. Request help proving the following: \; P_n(1-x) = -1^nP_n(x).