Suppose Yi, i=1, 2, ,…,n, are i.i.d. random variables, each
distributed N(2,25). Compute
Pr(0 < < 2) for a sample size of 9.
Please answer this question with a graph
Suppose Yi, i=1, 2, ,…,n, are i.i.d. random variables, each distributed N(2,25). Compute Pr(0 < <...
Consider the regression model where the εi are i.i.d. N(0,σ2) random variables, for i = 1, 2, . . . , n. (a) (4 points) Show βˆ is normally distributed with mean β and variance σ2 . 1 1SXX Question 6 Consider the regression model y = Bo + B12 + 8 where the €, are i.i.d. N(0,0%) random variables, for i = 1,2, ..., n. (a) (4 points) Show B1 is normally distributed with mean B1 and variances
We have N i.i.d random variables from the uniform distribution between 0 and 1. If N=1, what is the probability that the nth order statistic is less than or equal to the value x? (In other words, what is Pr(X(n)1≤x)?)
2. Suppose Xi,X2,..., Xn are i.i.d. random variables such that a e [0, 1] and has the following density function: r (2a) (1a-1 where ? > 0 is the parameter for the distribution. It is known that E(X) = 2 Compute the method of moments estimator for a
Suppose that the random variables X,..Xn are i.i.d. random variables, each uniform on the interval [0, 1]. Let Y1 = min(X1, ,X, and Yn = mar(X1,-..,X,H a. Show that Fri (y) = P(Ks y)-1-(1-Fri (y))". b. Show that and Fh(y) = P(, y) = (1-Fy(y))". c. Using the results from (a) and (b) and the fact that Fy (y)-y by property of uniform distribution on [0, 11, find EMI and EIYn]
6. Suppose random variables Z, are exponentially distributed: ZiExp(2) for i 1,2,..., n. Assume that the random variables Z, are independent. For each of the following functions of the Zi, find the expectation E] and variance Var[ ]. (a) 3 Z1- (b) 1.5Z1 +222-3 (c) i 32 (simplify, but final answer is an expression)
Let Yi, Y2,.... Yn denote independent and identically distributed uniform random variables on the interval (0,4A) obtain a method of moments estimator for λ, λ. Calculate the mean squared error of this estimator when estimating λ. (Your answer will be a function of the sample size n and λ
Let Yi, Y2,.... Yn denote independent and identically distributed uniform random variables on the interval (0,4A) obtain a method of moments estimator for λ, λ. Calculate the mean squared error of this estimator when estimating λ. (Your answer will be a function of the sample size n and λ
2. Suppose that we have a random sample of normally distributed random variables: X;2.2.4. N (u,02) for i = 1...n Derive the maximum likelihood estimators of u and o2.
Let Xi’s are i.i.d Poisson(λ) random variables for 1 ≤ i ≤ n. Derive the distribution of sum(Xi) i=1 to n
1.2 Let Yi and Y2 be independent random variables with Yi N(0, 1) and Y2 N(3,4). (a) What is the distribution of Y?? (b) If y-l (Y2-3)/2 | , obtain an expression for уту. What is its Yi and its distribution is yMVN(u, V), obtain an expression for yTV-ly. What is its distribution?