Problem 3.5: The density function of a continuous random variable X is shown below. Find (a) the mode. (b) the median, and (c) the mean. (0.9391 sin(√2-1) for 0.8 < x < 2.2 elsewhere
Q: Find the value of k.
A: NOTE-AS PER POLICY I HAVE CALCULATED FIRST MAIN QUESTION ONLY KINDLY REPOST OTHER QUESTION AGAIN…
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Q: Problem 4) For the following random variable X. (0 Fx (x) = { 0.4 0.8 1 x0}. c) Find E[XB].
A: Hi! Thank you for the question. As per the honor code, we are allowed to answer three sub-parts at a…
Q: 3.5: The density function of a continuous random variable X is ow. Find (a) the mode. (b) the…
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Q: shown below. Find (a) the mode. (b) the median, and (c) the mean.
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Q: a Which of the above estimators are unbiased for 0? e80.0 b Among the unbiased estimators of 0,…
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Q: shown below. Find (a) the mode. (b) the median, and (c) the mean. 0.9391 sin(√2x - 1) for 0.8 <x<2.2…
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- Problem 7 Let X1, X2, . . . , X10o be a random sample from a uniform distribution on the interval (0,1). Let S = X1 + X2 + . + X10 (1). Find the pdf for the statistic X(1) = min(X1, X2, ..., X100). (2). Find the pdf for the statistic X(100) max(X1, X2,..., X100). (3). Find an approximation for P(S > 55). (4). Let X = S/100. Find an approximation for P(2 < X < 2.15).71. Suppose we have a random sample X₁, X2, ..., Xn from an Exponential distribution with mean 1/A. Suppose we want to estimate the mean 1/A. One estimator for 1/X is T₁ = X. Of interest is to note that the minimum of X₁, X2,..., Xn, say X(1), has an Exponential distribution with mean (n)-¹. (a) Show that T₁ is an unbiased estimator of 1/A. (b) Find the constant a such that T₂ = aX(1) is an unbiased estimator of 1/X. (c) Since T₁ and T₂ are both unbiased we prefer the estimator with smaller variance. Which of the estimators T₁ and T₂ would you choose for estimating the mean 1/X?
- QUESTION 2 Suppose X has a continuous uniform distribution on the interval [-1,3]. Find the variance, o² var(X), of X. Round to 4 decimal places if needed. =Problem 4 Let X be a continuous random variable with PDF z' (2z +) 0 < x <1 fx(x) : otherwise If Y = +3, find Var(Y). %3D1.4 The pH of milk samples from Dairy Belle is a random variable Y with probability density function given by ((1/9)(4 – y)?,5Problem 1: The density function of a continuous random variable X is shown below. Find (a) the mode. (b) the median, and (c) the mean. f(x) = (0.9391 sin(√2-1) for 0.8 < x < 2.2 0 elsewhere1. The density function for random variable X is f(x). Find variance for the random variable X. Leave your answers as reduced fractions. f(x) = {16 x+04-52. If f(x) =e ,- coQuestion # 4: Let Y = X2, and let X be a uniform RV over (-1,1), find the Linear Mean Square Estimator of Y in terms of X and its mean square error.4.2-4Question 4 X1, X2, ..., Xn are i.i.d. random variables from N(0,0) distribution. Here, 0 = o² > 0 is the variance of the distribution, and is an unknown parameter. Find the MLE of 0 (no need to calculate the second derivative).Recommended 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