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Q: 2) Suppose that X is a random variable having a probability density function là) xe * = {(17) f(x;…
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- Question 9 Consider a Binomial Distribution of B(2,323, 0.294) Find the Expected value for the number of successes (or mean) for the probability density function.Suppose a random variable X has a Bernoulli distribution for which the parameter O is unknown (0Suppose that X has a Weibull distribution with β = 2 and δ = 2400. Determine the following. a. P(X > 5000) = b. For an exponential random variable with the same mean as the Weibull distribution P(X > 5000) =A random variable X has density 3x2 for 0 < x < 1. Find its variance.(use a decimal number, rounded to the nearest 1,000th. For example, 0.123)Suppose that X follows a Binomial distribution, i.e., X ∼ Binomial(3, 0.5). Define a new random variable as Y = X 2 , then, what is the value of the PMF of Y evaluated at 1, i.e., what is Pr(Y=1)? a). 0.3125 b). 0.25 c). 0.375 d). 0.5D5) This exercise uses the normal probability density function and requires the use of either technology or a table of values of the standard normal distribution. The cash operating expenses of the regional phone companies during the first half of 1994 were distributed about a mean of $29.92 per access line per month, with a standard deviation of $2.15. Company A's operating expenses were $28.00 per access line per month. Assuming a normal distribution of operating expenses, estimate the percentage of regional phone companies whose operating expenses were closer to the mean than the operating expenses of Company A were to the mean. (Round your answer to two decimal places.) %If z is a standard normal random variable and P(-zyIs the following random variable discrete or continuous? Let X represent the number of books in a random professor's office.Assume that you want to estimate an unknown parameter by using a noisy received signal for which you know the mean value and the covariance matrix of the noise but not its probability density function (pdf). You also know that the relationship between the unknown parameter and the received signal is linear. Would you use the BLUE estimation method, or the Maximum Likelihood estimation method? Justify your answer.Two six-sided dice are rolled and the scores added together. Draw thesample space, the probability density function and the cumulativeprobability density function by hand. ii. Recent news reports have found that, despite high vaccination rates,around 40% of new positive COVID tests are found in a particular groupof vaccinated individuals. How might Bayes’ Law and the law of totalprobability be useful in thinking about these results? iii. Use either the letters in your surname or numbers in your student idcard to explain the difference between “permutations” and“combinations.” Give a real-world example where the distinctionbetween permutations and combinations is crucial.A Histogram for SO2 emissions data (ton/days with 100 recorded readings is constructed with a width of class interval equal to 5. The maximum frequency is equal to 25 corresponds to class interval 5-20. The probability density corresponding to this interval isShow full answers and steps to this exerciseRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON