A continuous variable Y has a probability density function given by p(y)=Ay^3 for 0≤y≤3 What is the probability that we find Y=3?
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A continuous variable Y has a
What is the probability that we find Y=3?
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- Suppose ? and ? have joint probability density function ?(?, ?) = { ?(?^2 + ???), 0 ≤ x ≤ 1, −1 ≤ ? ≤ 1, 1 ≤ ? ≤ 2 0, elsewhere. a. Find ?. b. Find ?(0.5 < ?, 0 < ? ≤ 1, ? < 1.5. Please answer this question step by step and justify your solutionsOn a production line, parts are produced with a certain average size, but the exact size of each part varies due to the imprecision of the production process. Suppose that the difference between the size of the pieces produced (in millimeters) and the average size, which we will call production error, can be modeled as a continuous random variable X with a probability density function given by f(x) = 2, 5e^(-5|x|), for x E R (is in the image). Parts where the production error is less than -0.46 mm or greater than 0.46 mm should be discarded. Calculate (approximating to 4 decimal places): a) What is the proportion of parts that the company discards in its production process? b) What is the proportion of parts produced where the production error is positive? c) Knowing that for a given part the production error is positive, what is the probability of this part being discarded?The bearing capacity of the soil under a foundation is measured to range from 200 kPA to 450 kPA. The probability density within this range is given by engineering office as f(x) = 3 ,200< x < 450 450 ,otherwise If you know that the column on which stands is designed to carry a load 275 kPA, what is the probability of the failure of the foundation? Do you think redesigning project is necessary?
- please prove that the t-distribution is normalized. I believe this is done by integrating over -infinity to infinity but I got super thrown with that gamma function in there. Thanks!The "kernel trick" is a quick way to integrate when you can recognize a distribution in some equation g(x) which you want to integrate. It takes advantage of the fact that the pdf f(x) of a proper probability distribution must integrate to 1 over the support. Thus if we can manipulate an equation g(x) into the pdf of a known distribution and some multiplying constant c in other words, g(x) = c · f(x) --- then we know that C • --- Saex 9(x)dx = c Smex f(x)dx = c ·1 = c Steps: 1. manipulate equation so that you can recognize the kernel of a distribution (the terms involving x); 2. use the distribution to figure out the normalizing constant; 3. multiply and divide by the distribution's normalizing constant, and rearrange so that inside the integral is the pdf of the new distribution, and outside are the constant terms 4. integrate over the support. The following questions will be much easier if you use the kernel trick, so this question is intended to give you basic practice. QUESTION:…suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then P(X>1)
- The probability that a trainee will remain with a company is 0.6. the probability that am employee earnsbmore than k10,000 per month is 0.5. the probability that an employee who is a trainee remained with the company or who earns more than k10,000 per month is 0.7. what is the probability that an employee earns more than k10,000 per month given that he is a trainee who stayed with the companyA continuous variable X has a probability density function given by p(x)=Ax^2 for 0≤x≤4, and p(x)=0 otherwise. What is the value of the normalisation constant, A?The random variable X, the particle size (in micrometers) distribution is characterized by the probability density function:f(x) = 3x^(-4) , x > 1 and 0 elsewhereFind the probability that X exceeds 1.8 micrometers?
