10. Two random variables X and Y take on the values i and 2' with probability 1/2' (i = 1,2, .. .). Show that the probabilities sum to one. Find the expected value of X and Y.
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- Where does the z=2 come from? Just from X, and Y also being random variables?Suppose that three random variables x,„X,„X, fom a random sample from the uniform distribution on the interval [0,2], and they are independent. Determine the value of E(2X, –3X, +X,-4). Var(2X,–3X,+X, -4) and E(2x, –3X, +X, -4)°]Please
- Z and T are random variables that are normally distributed. The Mean of Z is 5 and its standard deviation is 3. The Mean of T is -2 and its standard deviation is 6. what's r and e, both greater than 0 so that P(4 < T < 16) =P(r< Z < e)https://ubs.ikc.edu.tr/MES/Application/Public/OnlineExam?examid=5604# - Opera VPN ubsikc.edu.tr/MES/Application/Public/OnlineExam 3. Soru 10 PO fx, (x) = 0.1 0.95- Ix, (2) = (")0.1"0.0"-, fx3 (x) = 0.5° Suppose that the random variable X is defined as X = 10(X-X2+X3) where the probability distributions of the independentYou are given n observations X1, X2, · · · , Xn that are i.i.d. and follow a geometric distribution with an unknown parameter θ which represents the probability of a success. Find the Maximum Likelihood Estimator of the parameter θ.
- 2. Let X be a random variable with p.m.f., (1+ x? f(x) = -,x = -1,0,1,2,3 20 0 ,otherwise. Find E(3X2 + 6).If x is a random variable that has a uniform distribution in the interval [1,7].[1,7]. What is the probability of the random variable x taking on values greater than 4?Suppose that the unknown X is uniformly distributed between 0 and 2. What is the expected value of (4X3 + 1)?
- If the joint probability distribution of X and Y isgiven byf(x, y) = 130 (x + y) for x = 0, 1, 2, 3; y = 0, 1, 2 construct a table showing the values of the joint distribu-tion function of the two random variables at the 12 points (0, 0),(0, 1), ... ,(3, 2).3. Let X be the random variable that takes on the integers {0, 1, 2, ..., 15} with equal probabilities. Define a new random variable Y = X + A, where A is a random variable that takes on the values {-1, 0, 1} with equal probabilities. If the RVs X and A are independent, find the mutual information between X and Y.Q3. Let X and Y be two independent random variables, each representing the number of trials until the first success in a sequence of Bernoulli trials. Evaluate P(X = Y) assuming that the probability of success in a single trial(in case of X and Y both) is 0.4.