The PSD of random process is given by lol < 1 dxx(@) = 0, elsewhere Find its autocorrelation function.
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- Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.A Nail salon opens at 10am. During the busy Christmas period people start arriving at 9 am and queue in front of the salon to wait for the salon opening. The arrivals follow a non-homogeneous Poisson process with rate function A(t) = 25t^2. What the average waiting time of a person who is present at the nail salon at 10 am.If P(B) = ² and P(A'^B) = 12, for two events A and B, find P(A/B).
- A sample of 20 observations is taken from the normal distribution where the sample mean is 3. The normal distribution has a mean of 0 and a variance of e^beta. a)Find the estimator for the method of moments for beta and the numerical value of it?You have two random variables M and N where the joint pdf is given by f_M,N(m,n) = 1/2 if m + n >=2, m <=2 and n <=2 and 0 o/w. What is the cdf?None
- A random sample of n volumes in the form of X1, X2 . , Xn is .. taken from a population with parameters 0, and 02 with a continuous uniform distribution. Let the 0, parameter be known. Based on this random sample, obtain the Maximum Likelihood Estimator ^@Mle of parameter 02.Obtain 100 (1 x)% confidence limits (for large samples) for the parameter 2 of the f(x, 2) = e-^.^* ; x ; x = 0, 1, 2,... x! Poisson distribution:Please answer asap, dont need to find numerical value just an expression.Thank You f_X refers to the standard p.d.f., so f_X(x)=(1/sqrt(2pi)) e^{-x^2/2}
- Heteroskedasticity arises because of non-constant variance of the error terms. We said proportional heteroskedasticity exists when the error variance takes the following structure: Var(et)=σt^2=σ^2 xt. But as we know, that is only one of many forms of heteroskedasticity. To get rid of that specific form of heteroskedasticity using Generalized Least Squares, we employed a specific correction – we divided by the square root of our independent variable x. And the reason why that specific correction worked, and yielded a variance of our GLS estimates that was sigma-squared, was because of the following math: (Picture 1) Where var(et)=σ^2 according to our LS assumptions. In other words, dividing everything by the square root of x made this correction work to give us sigma squared at the end of the expression. But if we have a different form of heteroskedasticity (i.e. a difference variance structure), we have to do a different correction to get rid of it. (a) what correction would you use…The probability density function of the random variable X is as in the picture with λ> 0. Investigate whether the most likelihood estimator (λ^) of λ is neutral. hint : ?(?) = √??/2 and ?(?²)=2?Suppose X1, ..., Xn have been randomly sampled from a normal distribution with mean 0 and unknown variance sigma^2, and let U = c * i=1 -> n summation (X_ i)^2 , where c is a constant. Find the value of c that minimises the Mean Squared Error (MSE)