Please solve this problem step by step.
Please solve this problem step by step. a discrete random variable vif C. 1z] , it...
Problem 5. Prove the following result for any number a and discrete random variable X. 티(X-a 21 = Var(X) + (E(X)-a)2 You must start your proof by using the definition of the expected value of a function of a discrete random variable, i.e. where g(x)- (x-a)
Let X be a discrete random variable with PMF(a) Find P(X ≤ 9). (b) Find E[X] and Var(X). (c) Find MX(t), where t < ln 3.
2. For a discrete random variable X, with CDF F(X), it is possible to show that P(a < X S b)-F(b) - F(a), for a 3 b. This is a useful fact for finding the probabil- ity that a random variable falls within a certain range. In particular, let X be a random variable with pmf p( 2 tor c-1,2 a. Find the CDF of X b. Find P(X X 5). c. Find P(X> 4). 3. Let X be a...
Big Question Please Help! Determine whether the value is a discrete random variable, continuous random variable, or not a random variable, a. The exact time it takes to evaluate 27 + 72 b. The number of bald eagles in a country c. The eye color of people on commercial aircraft flights d. The time it takes to fly from City A to City B e. The number of people in a restaurant that has a capacity of 200 f. The...
Please solve the problem step by step. Thank you! 1. (30 marks) Friedman's Permanent Income Hypothesis states that Y is non-stohastic p2 where Cpi and Ypi are permanent consumption and income, respectively (a) (10 marks) Derive the OLS estimator k. (Clearly setup the minimization problem and solve for the estimator) (b) (10 marks) Derive Var(k) (c) (10 marks) Prove that k is unbiased mathematically. (State the assumptions you use and where do they apply)
using excel answer the problem below Let X be a discrete random variable having following probability distribution. x 2 4 6 8 P(x) 0.2 0.35 0.3 0.15 Complete the following table and compute mean and variance for X x P(x) x· P(x) x2. P(x) 2 0.2 4 0.35 6 0.3 8 0.15 Total 1 Expected value E(X) = u = Variance Var = o2 =
Problem 3. Let X be a discrete random variable that takes values in N. Show that if X is memory-free then it must be the case that X Geo(p) for some p. (Hint a useful first step might be to show that P(X > t)= P(X > 1)' for all t E N.) Problem 3. Let X be a discrete random variable that takes values in N. Show that if X is memory-free then it must be the case that...
i need this step by step please Problem 9: Given X is a random variable with normal distribution, N (?, ?2). Given ?-6 and ?2-0.25, determine b, c, and d such that: I. P (Xs b) - 0.05 Il. P (X2 c) 0.40
1. The probability distribution of a discrete random variable X is given by: P(X =-1) = 5, P(X = 0) = and P(X = 1) = ? (a) Compute E[X]. (b) Determine the probability distribution Y = X2 and use it to compute E[Y]. (c) Determine E[x2] using the change-of-variable formula. (You should match your an- swer in part (b). (d) Determine Var(X).
Problem 3 A discrete random variable Y takes values {k= 0, 1, 2, ...,} such that PLY Z k} = ()* for k 20. 1. Derive P[Y = k) for any k > 0. 2. Evaluate expectation, E[Y] = 3. Given E[Y(Y - 1)] = 15 , find variance of Y, Var[Y] =