A WSS random process X(f) has psd Sx(@) XX a* +10@ +9 Find the autocorrelation and mean square value of the process.
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- A potato chip company produces a large number of potato chip bags each day and wants to investigate whether a new packaging machine will lower the proportion of bags that are damaged. The company selected a random sample of 150 bags from the old machine and found that 15 percent of the bags were damaged, then selected a random sample of 200 bags from the new machine and found that 8 percent were damaged. Let pˆOp^O represent the sample proportion of bags packaged on the old machine that are damaged, pˆNp^N represent the sample proportion of bags packaged on the new machine that are damaged, pˆCp^C represent the combined proportion of damaged bags from both machines, and nOnO and nNnN represent the respective sample sizes for the old machine and new machine. Have the conditions for statistical inference for testing a difference in population proportions been met? No, the condition for independence has not been met, because random samples were not selected. A No, the…(8) Find the variance of X when X is distributed as N(0, 1). The correct answer is -1 1 N/A (Select One)Show that variance o? = (x²) – ((x))²
- Suppose that the random change in value of a financial asset is X over the first day and Y over the second. Suppose also that Var(X) =18 and Var(Y) = 26 In this case, the total change in the value over these two days is given by X +Y. Do you have enough information to compute Var(X +Y)? If so, compute this value. If not, explain what additional information you need to do so.Calculate the variance of a random variable X whose characteristic function is (1+ e3it)² f(t) = 4A random variable X has only two values a and b with P(X = a) = p , P(X = b) = q (p + q = 1).Find its mean value and variation.
- Many people believe that the daily change in price of a company's stock in the stock market is a random variable with mean 0 and variance o² during the middle 2 months between 2 earning report dates when there is not much news released. That is, if Yn represents the closing price of the stock on the nth trading day of that period, then Yn = Yn-1+Xn, for 1 ≤ n ≤ 60, where X₁, X2,..., X60 are independent and identically distributed random variables with mean 0 and variance o². Suppose that the stock price at the beginning of the 2-month period is 100. If o = 2, what is the approximate probability that the stock's closing price on the 30th trading day will exceed 110, i.e., what is P(Y30 > 110)A random variable X has the following PMF: [refer to image] a) Find E(X) b) If Y = g(X) = X^2, calculate the PMF of Y and draw the CDF of YSuppose that lifetime of bulb of type n is exponentially distributed with mean value n years, where n = 1, 2, 3, 4, 5. A bulb is equally likely be chosen from these five types. (a)Find the probability that the selected bulb can survive for at least 3 years. (b)Find the variance of the lifetime of the selected bulb.
- Assume that the entire sample has 2 positive observations and 6 negatives observations. Variable X1: at the left branch has 2 positive observations and 4 negatives observations;at the right branch has 6 positive observations and 6 negatives observations. What is the information gain or reduction in uncertainty of X1 using the Gini index? (round to two decimal spaces)Identify the two procedures that can be used to compute the Spearman correlation.Show that the mean of a random sample of size n from an exponential population is a minimum variance unbiased estimator of the parameter 0.