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)
I need help with parts “c”, “d, and “e” thanks.
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)
Find: (a) a. X = 0 1 p(y) Y = 0 1 2 .10 .25 .25 .05 a .25 p(x) (b) The marginal probabilities for X and Y. (c) P(Y= 1/X = = 1).
If X has an F distribution with ν1 and ν2 degrees offreedom, show that Y = 1Xhas an F distribution with ν2 and ν1 degrees of freedom.
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.
Q3. For simplicity assume only two states of the world S = subjective states and ignores the actual distribution of probabilities. Formally, the value of an act f is {S1, s2}. Suppose a consumer evaluates the AA acts as an average of the best possible payoffs across th V(f) = 0.5 (max{z: f(s1)(z) > 0} + max{z : f(s2)(z) > 0}), where f(s)(z) is a probability of prize z in state s and max{z : f(s)(z) > 0}is the greatest prize possible (with some positive probability) in state s. Consider the following example of how such consumer evaluates acts f and g below: 0.2 0.8 1.0 0.5 0.5 0.3 0.7 00 01 90 30 20 50 The highest payoff of act f in s1 is 100 and the highest payoff of act f in s2 is 90, so the value of act f will be V(f) = 0.5(100 + 90) = 95. At the same time, the highest value of act g in s1 is 30 and the highest value of act g in s2 is 50, so the value of act g is V(g) = 0.5(30 + 50) = 40. Note that this is only an example, and in what follows you have to consider all possible acts.…
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
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