-0.1 2- X(1) to 0.05 to + 0.1 lo + 0.2 In the random pulse sequence shown above, pulses may occur or not occur with equal probability at periodic time intervals of 0.1 second. The reference time to for any sample function is a random variable uniformly distributed over the interval of 0.1 second. a) Find the mean value of this process. b) Find the variance of this process. c) Find the spectral density of the process.

In a poisson distribution P(X=0) = P(X=2).Find the variance V(X) of X.

Suppose that the contagious period of COVID-20 has an average of 7 days, and follows a chi-square distribution.  Let X measure the contagious period for a randomly selected specimen of the COVID-20 virus. State the distribution of the random variable X. Group of answer choices X∼χ2(6) X∼Student′st(7) X∼χ2(7) X∼Continuous(7)     A friend of yours has COVID-20 and the doctors have told her that she has had it for 10 days.  Compute the probability that they are still contagious.  (I.E. compute the probability that X is greater than or equal to 10 days.)

We have the following information regarding the random variables X, X, and X3: Var(X1) = Var(X2) = Var(X3), Px, X2 = 0.2, pxX, = 0.5, px X Calculate the correlation between X+ X3 and X2 + X3. (i.e. calculate px+Xs.X2+X3) 0.9. %3D

​(c) Calcculate d and sd ​(d) Find the standardized test statistic t.

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