The distribution law of the random variable X is given by
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Since one seed planted may or may not germinate, the number of sprouts out of 3 seeds planted X will be a random variable with a binomial distribution. The values of the random variable X are x1=0; x2=1, x3=2, x4=3, and we find the probabilities of accepting these values using Bernoulli's formula: Solution:
Since the number of bulbs is large and the probability of failure is small, it is convenient to use Poisson's formula. Since n=10000, p=0.0001, =pr=1, k=0, 1, 2, 3, 4, based on Poisson's formula:
Find the mathematical expectation, variance, root mean square average of a random variable. М(Х)=100,1+120,2+200,1+250,2+300,4=1+2,4+2+5+12 =22,4. М(Х2)=1000,1+1440,2+4000,1+6250,2+900×0,4=10+28,8+40+125+360=563,8. D(Х)=М(Х2)–[М(Х)]2=563,8–(22,4)2=62,04. Problems.
According to the condition of the problem D(X)=0.04; M(X)=100 and 99.5≤X≤100.5. We subtract M(X) = 100 from this inequality: –0,5≤Х–М(Х)≤0,5 We get the inequality |X–M(X)|≤0.5 which is as strong as this inequality. Here =0.5. We use the Chebyshev inequality: , р>0,84
We denote the number of standard products by X and find M(X), D(X) and . Standard products. It is 98%. So, p=0.98, non-standard probability q=00.02; Based on the formulas M(X)=pr and D(X)=prq we find: M(X)=10000.98=980, D(X)=10000.980.02=19.6 . Subtract M(X) =980 from both sides of the inequality 970≤X≤990, which follows from the condition of the problem: –10≤Х– М(Х) ≤ 10, |X–M(X)|≤10. From here, taking into account that =10, we find based on the Chebyshev inequality: , Р>0,804.
According to the condition of the problem p=2000, D(X)=S = 9, =0.3 If we call the yield per hectare a random quantity (X1 - from the first hectare, X2 - from the second hectare, etc.), then it will be the average yield. If M(X1), M(X2), . . ., M(Xp) is the average productivity per hectare, then based on Chebyshev's theorem
We use Bernoulli's theorem to solve this problem. According to the condition of the problem: R=0.025 (2.5% brack details), q=1–r=0.975, =0.005. Then according to Bernoulli's theorem:
We use Bernoulli's theorem to solve the problem. Should be ≥0.98. Here we find n: ≤0, 02 or So, it is necessary to conduct at least p=1200 experiments.
We also use Bernoulli's formula to solve this problem. We have the following: , P=0,8; q=1–p=0,2; q=5000 , 0,02 Download 56.84 Kb. Do'stlaringiz bilan baham: |
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