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- Let X1, X2, .,X25 be i.i.d. random variables from Po(5). Estimate the MSE for the median estimator using Monte Carlo estimation.What is the variance of 1, 3, 5, and 7? Show your solutionPROBLEM 3 The PDF of a random variable X is given in the picture below K is 2 Find the correct value of c. Find the variance of the given random variable. Find P(X<2).
- Question 3 Suppose that the current measurements in a strip of wire are assumed to follow a normal distribution with a mean of 10 milliamperes and a variance of 4 (milliamperes)?. what is the probability that a current measurement is between 5 and 9 milliamperes?The first principal component is a normalized linear combination of the original variables with the largest varianceTrueFalseWhat is the likelihood ratio p(x|C₁) p(x|C₂) in the case of Gaussian densities?
- For a Binomial distribution mean is 6 and standard deviation is Rt(2). Find the first two terms of the distribution.Solve in R programming language: 5) Use R to calculate and simulate with the exponential distribution as follows. (a) For an exponential random variable X with λ = 4, simulate 1000 independent exponential random variables by using the R function rexp(n, λ). Calculate the mean and variance of this sample. (b) Compare the empirical results from part (a) with the distribution mean 1/λ and the distribution standard deviation 1/λ.Let X be a random variable with density function 1) ={0. k(1 -x), if 0<*<1; otherwise. f(x) Find k, together with the expectation and the variance of the random variable Y defined as Y = 3X - 1.
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