6. The probability W (n) that an event characterized by a probability p occurs n times in N trials wasshown by binomial distributionW(n) =Consider the situation where the probability p is small and n << N(a) Show that (1-p)N-ne-Np(b) Show thatN!(N − n)!(c) From (b) show it reduces to≈N"N!n!(N-n)!P" (1-p) N-nW(n):where A = Np(d) From (c), show that properly normalized(e) Calculate the mean and variance=1²n!ext

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Answered: 6. The probability W (n) that an event…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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3. (a) A city has sunny weather on 3 out of every 5 days on average. Use the binomial formula to find the probability that exactly 4 days out of a 7 day week are sunny. Binomial formula P(x) = Cx p* (1-p) * for x = 0, 1, 2, ..n where Cx,n=n! / [ x! (n-x)!] and n! = n(n-1)(n-2) ... (2)(1) Note: 0! = 1 P(4) = (b) In a certain region, there is a 1/3 probability of a hurricane occurring in a given year (i.e. an average of 1 every 3 years). Use the binomial formula to find the probability that exactly 2 hurricanes occur in the next 10 years. P(2) = (c) Use the Poisson formula to find the probability that at least 2 hurricanes occur in the next 5 years: P(x) = (a t) e-it x! P (22) =
When a man observed a sobriety checkpoint conducted by a police department, he saw 656 drivers were screened and 5 were arrested for driving while intoxicated. Based on those results, we can estimate that P(W)equals=0.00762,where W denotes the event of screening a driver and getting someone who is intoxicated. What does P(W) denote, and what is its value? What does P(W) represent? P(W)=
The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20-39 who regularly skip eating breakfast is 0.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size n = 500 of young adults ages 20-39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, X, in Lance's sample who regularly skip breakfast is greater than 122. You may find table of critical values helpful. Express the result as a decimal precise to three places. P(X > 122)%3D eal limir thaor tnr the hinamialdietrikotian tn indtha neohabilin: tbot the numbar of individuale in Aanly tha nd tems of use contact us he p about us cyeers 6:56 PM 11/6/2020 a. 2) Cip prt sc insert 110 |
only HANDWRITTEN answer needed ( NOT TYPED)
() Show that PM) = -y + 1)P> 1 if y P(y - 1) if y is small (y (n + 1) p). Thus, successive binomial probabilities increase for a while and decrease from then on. Ply - (n + 1)p > y yg (n +1- y)p > y + n+1 (n +1- y)p > (n +1- y)P > 1 yq Show that_P) PŮY – 1) (n + 1)p (n + 1) p. (n +1- y)p Ply - 2) > Also for y 2 (n + 1)p, then p(y) z > P(y + 2) > . Thus it is clear that p(y) is maximized when y is as close to p as possible.
which expressions correctly describes the experimental probability, P(B), where n(B) is the number of times event B occurred and n(T) is the total number of trials, T, in the experiment? a) P(B) = n(B) x n(T) b) P(B) = n(N) + n(T) c) P(B) = n(T)/n(B) d) P(B) = n(B)/n(T)
Let X be a random variable that can take values x = 2,4,6,8 and has probabilities given by the function P(X = x) = 3x/60 Find (1) P(X = 4) (2) P (X ≤ 6) (3) P(X < 6) (4) P (X ≥ 3)
The graph of the discrete probability to the right represents the number of live births by a mother 49 to 53 years old who had a live birth in 2015. Complete parts (a) through (d) below. 0 1 (a) What is the probability that a randomly selected 49- to 53-year-old mother who had a live birth in 2015 has had her fourth live birth in that year? (Type an integer or a decimal.) (b) What is the probability that a randomly selected 49- to 53-year-old mother who had a live birth in 2015 has had her fourth or fifth live birth in that year? (Type an integer or a decimal.) (c) What is the probability that a randomly selected 49- to 53-year-old mother who had a live birth in 2015 has had her sixth or more live birth in that year? (Type an integer or a decimal.) Statcrunch no JL @ 1 # с $ % JI JU & 0.30 0.25 0.20 0.15 0.10 0.05- 0.00 U 165 0.112 0.094 Number of Live Births 7 R # 8 A G
Suppose Xt denotes the unknown whose value is the success count for ?ttrials of a Bernoulli Process with success rate p and Wn the unknown whose value is the number of trials to have the nth success. Then, the probability that the number of trials to get the 7th success is at most 10 is which of the following? (A) P(X10≥7)P(X10≥7) (B) P(X7<10)P(X7<10) (C) P(X10<7)P(X10<7) (D) P(W7≥10)
X is a normally distributed random variable with mean 72 and standard deviation 22. Use calculator to find the probability indicated. a) P(78<X<127) b) P(60<X<90) c) P(X=80) *continuous

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