Let X, the number of micro-flaws on the surface of a randomly selected, freshly painted car door of a certain type, have a Poisson distribution with parameter u = 5. Find P(4
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- Assume that the weight of hamsters is Normally distributed with μ = 1.2 lbs and σ = 0.25 lbs. Suppose I randomly select 5 hamsters. What is P(X < 1.15)? (Use 3 decimal places)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 λ = 3. The profit per foot when the rope is sold is given by X, where X = 60 - 4Y - y². Find the expected profit per foot. $ per footLet X has Poisson distribution with parameter 2 such that P(X=2) =9P(X=4) +90P(X=6). Find the value of parameter
- Let X ~ U[0,1] and Y = -βln(1-X). What is the distribution of Y? Justify.The data below shows the maximum temperature (e) and ike number of bau's of Soupe sold at Gd's Gtrace Canteen on eleven randomly tset last year. Selected degs. (2345 67891011 32362229251811|1685 2 Boesls Sslell2/21010203545 Sosos763 Day üfind tke mean maximum tamperature, y of Soup recorded. ) Plot and label the poit M en the Scatter diagram. Ca) Re line of passes throigh The point M and thhe y-intercept (0,33.2). Draw his line on your graph. lw Find the equation of the line of best On another day of the year, the tumperature was 20€. Uong the equation of the line estimate e nuinber Seld on that day. best fit fr the data fit of best it, of bouls3 a. Let X have a Poisson distribution with a mean of 3. Define Y = (X-3) ^2 , specify pdf from Y.b. Let Y have a Poisson distribution with a mean of 5. Define Y=Z+X where Z and X are independent, where X is a random variable at point a, determine the distribution and pdf of Z.
- Let X denote the number of paint defects found in a square yard section of a car body painted by a robot. These data are obtained: 8. 5 10 3 1 12 2 7 9 Assume that X has a Poisson distribution with parameter As. а. Find an unbiased estimate for As. b. Find an unbiased estimate for the average number of flaws per square yard. C. Find an unbiased estimate for the average number of flaws per square foot.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.Let X1, X2, X3 be a random sample from a distribution with p.d.f. f(x; 8) = e-(-0) I(8,00) (). Here we use the indicator function of set A defined by I4(æ) = 1, when a E A, zero, elsewhere. Let Y be the first order statistic and let Y be the third order statistic. Then, Select one: O a. Y is sufficient and Y is sufficient. O b. Y is sufficient and Y is not sufficient. O c. Y is not sufficient and Y, is not sufficient. O d. Y, is not sufficient and Y, is sufficient.
- Let X1, . . . , Xn be iid from Exp(β). Find the distribution of the sample maximum Y = X(n). Is this an exponential distribution? (This question was rejected this morning. I did double check and there is no missing info with this question.)Let X1, X2,...X100 be the annual average temperature in Paris in the years 2001, 2002, ..., 2100, respectively. Assume that average annual temperatures are sampled i.id. from a continuous distribution.(Note: For this problem, we assume the temperature distribution doesn't change over time. With global warming, this is not a good assumption.)A year is a record high if its average temperature is greater than those in all previous years (starting with 2001), and a record low if its average temperature islower than those in all previous years. By definition, the year 2001 is both a record high and a record low.1. In the 20 century (the years 2001 through 2100, inclusive), find the expected number of years that are either a record high or a record low.2. Let N be an r.v. representing the number of years required to get a new record high after the year 2001. Find P(N > n) for all positive integers n, and use thisto find the PMF of N.3. Check answers to parts (1) and (2).4. Explain how…let Y=5X+10 and X be normally distributed with a mean 10 and varience 25. find P(Y<54).
