Two random variables X and Y are known to be uncorrelated. When considered separately, X is known to be uniform in the interval [0, 4], while Y is Gaussian distributed with mean 2 and variance 2. Find the joint expectation E[XY]
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Two random variables X and Y are known to be uncorrelated. When considered separately, X is known to be uniform in the interval [0, 4], while Y is Gaussian distributed with mean 2 and variance 2. Find the joint expectation E[XY]
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- Suppose you have a sample of 9 observations Y1,...,Y, from a normal population with mean 2 and variance 4. Let Y and S denote the sample mean and sample variance, respectively. What is the distribution of E ( (a) (b) 653 (c) Suppose X1,X2, X3, X4, X5 are independent random variables from a normal population with mean 0 and variance 4. Define S3 = E(X, - X). What is the distribution of 253 + S3?Consider a Gaussian random variable with mean equal to 3 and variance equal to 5, then the PDF of X has equal values at: O x = 5, x = -5 x = 1, x = -1 O x = 3, x = - 3 O x = -2, x = 2 O x = 2, x = 4Compute for the variance and standard deviation of the population
- Suppose that X₁, X₂, Xn and Y₁, Y2, . Yn are independent random samples from populations with means ₁ and ₂ and variances of and o2, respectively. Show that X - Y is a consistent estimator of μ₁ - 2.Im stuggling with this question, posted a screen shot below. Please help :)Given (x + 2y) ,0With an American penny, the likelihood of getting H when it is spun on edge is 0.3. If X is the random variable where X(H ) = 1, X(T ) = −1, find the expected value E(X), the variance, Var(X), and express X in its standard form.2. The random variable X is the amount of fructose in apples (in ounces) grown at a local orchard and is represented by the following cdf: 2(x +), 1Suppose that X, Y and Z are independent. The expected value is given by E(X) = 0, E(Y) = 1, E(Z) = 5 We also know that the variance is given by Var(X)=1, Var(Y)=1, Var(Z)=25 The values of the covariance are Cov(X,Y)=2, Cov(Y,Z)=1 Which of the satements are true? 1. Cov(ex,Y2 + 1) = 0 2. Е(XY)-1 3. If a and b are real numbers then Cov(aX+bZ, Y+Z)=2a+25b 4. Cov(X,Y)=0Suppose that the number of customers entering a bank in one hour is a Poisson random variable and suppose that P(X=0)=0.02. Find the mean and variance of the variable. X: Number of customers entering a bank in one hour E(X)= Answer (Give the exact answer) V(X)= Answer (Give the exact answer) What is the probability that 5 customers will enter in two hours? Answer: Note: Answer with at least 4 decimal places2Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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