let k be a random variable that takes with equal prob 1/(2n+1), the values in integer the interval [-n, n]. Find the PMF of the random variable y = log (x) where X = a^k! and aso.
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![let k be a random variable that takes with
equal prob 1/(2n+1),
values in
integer
the interral' [-n, n]. Find the PMF of the
random variable y = log (x) where X = a¹" and
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- let x be a random variable with moment generating function Mx(t)=(0.6 + 0.4e^t)^20 then the variance of x isFind the mean of the random variable X with PDF S 3x² _if 0the random variable Y is such that : E(2Y+3)=6 and Var(2-3Y)=11 find E(Y^2)Consider a random variable Y with PDF Pr(Y=k)=pq^(k-1),k=1,2,3,4,5....compute for E(2Y)Suppose that Y1,Y2 are independent identically distributed (iid) random variables form a random sample from a probability distribution given by f(y)=θe^(−θy), y≥0 Suppose we observed a sample of size two (n=2): 0.04304550, 0.50263474. Read the data into R. Create a function in R to compute the log‐likelihood. Plot the likelihood function on a fine grid of θ values in R. Estimate the MLE of θ using Bisection, Secant, and Newton-Raphson methods in R.Suppose that f(x)=k/(4^x), x=1,2,3,... is the probability function for a random variable X. Find the value of 1/k.Prove that if M(t) is the MGF of a random variable X, then the MGF of a + bX is e^at M (bt)3. The length of time required by students to complete a 1 hour exam is a random variable with a pdf given by: f (x) = = ca + for 0 sæ<1 a. Find c. Enter c as a reduced fraction. C = b. Find F(x). Enter coefficients as reduced fractions and use ^ to denote powers. F(x) = c. Find the probability that a student takes less than 30 minutes to complete the exam. Enter the probability as a reduced fraction. prob = d. Find the median length of time to take the exam. Enter your answer in hours with 4 decimal places. median = hours e. Find the length of time for the first 10% of the students to complete the exam. Enter your answer in hours with 4 decimal places. hours answer = f. Find the expected value, variance, and standard deviation of X. Enter your answer in hours with 4 decimal places (or hours squared in the case of variance), hours expected value =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 mean and variance when the probability variable X's moment-generating function is as follows f(x)= 2x-1/16 , x=1,2,3,4 my answer is mean = 25/8, var = 170/16 - (50/16)^2 but solution is mean = 2, var = 4/5 How do we solve the problem? Help meLet X be a Gaussian random variable (0,1). Let M = e^(5*X) be a derived random variable. What is E[M]?Let X1,…,Xn be i.i.d. Exp(λ) random variables, where λ is unknown.What is the variance and quadratic risk of the unbiased estimator θ^ = n*mini(Xi).SEE MORE QUESTIONS