Let X, the number of flaws on the surface of a randomly selected boiler of a certain type, have a Poisson distribution with parameter μTables to compute the following probabilities. (Round your answers to three decimal places.)(a)P(X ≤7)(b) P(X = 7)(c) P(9 ≤ X)(d) P(5 ≤ X ≤7)(e) P(5 < x < 7)=5. Use the cumulative Poisson probabilities from the Appendix

Step 1: Find the appropriate poisson table to be used*Find the table with λ = μ = 5Only use the…

Answered: Let X, the number of flaws on the…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.3: Binomial Probability

Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...

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If a binomial experiment has probability p success, then the probability of failure is ____________________. The probability of getting exactly r successes in n trials of this experiment is C(_________, _________)p (1p)
The maintenance department in a factory claims that the number of breakdowns of a particular machine follows a Poisson distribution with a mean of 2 breakdowns every 428 hours. Let x denote the time (in hours) between successive breakdowns. (a) Find λ and Ux. (Write the fraction in reduced form.) ux = f(x) = 214 (b) Write the formula for the exponential probability curve of x. P(x <4) ✔ Answer is complete and correct. 1 P(115
3. Let Y be the number of speeding tickets a YSU student got last year. Suppose Y has probabilitymass function (PMF)y 0 1 2 3fY (y) 0.12 0.13 0.33 0.42(a) What is the probability a YSU student got exactly one ticket?(b) What is the probability a YSU student got at least one ticket?(c) Compute µY , the mean of Y .(d) Find the variance and standard deviation of Y .(e) What is the probability that Y exceeds its mean value?
3. Consider a Exponential Distribution with parameter of 0.0025 i.e. Exp(0.0025) B. Compute The following Probabilities V. P(x > 100 | x 100 ) C. Explain why the last 2 answers are different
2.3. The power output P in MW from a wind farm is a function P(w) = 3w² of the wind speed w in m/s. Suppose that the wind speed is uniformly distributed on the interval [5, 15]. %3D (a) What is the probability that the wind speed is at least 10m/? (b) What is the probability that the power output is at least 300 MW? (c) What is the expected power output E[P] (d) Suppose now that the wind turbines adjust for high wind speeds to reduce loading. This means that the wind farm has a maximum power output of 300 MW, so: 3w? w 10 What is the expected power output E[P] of the wind farm?
Many people believe that the daily change in price of a company's stock in the stock market is a random variable with mean 0 and variance o² during the middle 2 months between 2 earning report dates when there is not much news released. That is, if Yn represents the closing price of the stock on the nth trading day of that period, then Yn = Yn-1+Xn, for 1 ≤ n ≤ 60, where X₁, X2,..., X60 are independent and identically distributed random variables with mean 0 and variance o². Suppose that the stock price at the beginning of the 2-month period is 100. If o = 2, what is the approximate probability that the stock's closing price on the 30th trading day will exceed 110, i.e., what is P(Y30 > 110)
A certain process for producing an industrial chemical yields a product containing two predominant types of impurities. For a certain volume of sample from this process, let X1 denote the proportion of impurities in the sample and let X2 denote the proportion of type I impurity among all impurities found. Suppose the joint distribution of X1 and X2, after investigation of many such samples, can be adequately modeled by the following function: (see picture) a. Calculate the probability that X1 is less than 0.5 and that X2 is between 0.4 and 0.7. b. Show that these random variables are independent.
In an area having sandy soil, 40 small trees of a certain type were planted, and another 40 trees were planted in an area having clay soil. Let X = the number of trees planted in sandy soil that survive 1 year and Y = the number of trees planted in clay soil that survive 1 year. If the probability that a tree planted in sandy soil will survive 1 year is 0.5 and the probability of 1-year survival in clay soil is 0.4, compute an approximation to P(-4 < X – Y < 4) (do not bother with the continuity correction). (Round your answer to four decimal places.) In USE SALT .148
A biased die with five faces is rolled. The discrete random variable Y represents the score which is uppermost. The cumulative distribution (cdf) is shown in the following table. i)Provided that Pr(y= 2) = 0.2, find the value of k1 and k2. (ii) Sketch F(y). iii)Construct the pmf of Y and sketch it
9. The concentration function of a random variable X is defined as Qx(h) sup P(x ≤x≤x+h), h>0. (b) Is it true that Qx(ah) =aQx (h)?
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In the daily production of a certain kind of rope, the number of defects per foot given by Y is assumed to have a Poisson distribution with mean ? = 4. The profit per foot when the rope is sold is given by X, where X = 70 − 3Y − Y2. Find the expected profit per foot.

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