Question 2 0/1 point (graded) Now suppose that you have a random variable X, where E[X...
(1 point) For a random variable X, suppose that E[X] = 2 and Var(X) = 3. Then (a) E[(5 + x)2) = (b) Var(2 + 6X) =
1 point possible (graded) If Mx (t) = e-5(1-e'), find Var(X). Submit You have used 0 of 4 attempts Save
Please answer both. . Suppose that Y is a random variable with distribution function below. 1-e-v/2, 0, y > 0; otherwise F(y) = (a) Find the probability density function (pdf) f(y) of Y. yso (b) E(Y) and Var(Y) 5. Suppose X is a random variable with E(X) 5 and Var(X)-2. What is E(X)?
Suppose that X is continuous random variable with 2. 1 € [0, 1] probability density function fx(2) = . Compute the 10 ¢ [0, 1]" following: (a) The expectation E[X]. (b) The variance Var[X]. (c) The cumulative distribution function Fx.
Recall that the variance of a random variable is defined as Var[X]=E[(X−μ)2], where μ = E[X]. Use the properties of expectation to show that we can rewrite the variance of a random variable X as Var [X]=E[X^2]−(E[X])^2 Problem 3. (1 point) Recall that the variance of a random variable is defined as Var X-E(X-μ)21, where μ= E[X]. Use the properties of expectation to show that we can rewrite the variance of a random variable X as u hare i- ElX)L...
4) Suppose a random variable X has theprobability distribution with a: o 1 -2 0 1 2 0.3 0.1 p 0.4 . then p - ,P(X2 22) = ,, and E(X) = - 5) Suppose X~Bin(10,0.4), Y-2X+5, then E(Y) = ,Var(Y) 6) Suppose X-NC-3,4) and Y~N(2,9), X and Y are independent, then Var(X-2Y)
1. Consider a discrete random variable, X, where the outcome of this random variable is determined by throwing a 6-sided die. X takes on integer values 1,2,…,6. The die is fair. That is, P(X=1)= P(X=2)=…= P(X=6). i. Draw the probability distribution function for this random variable. Carefully label the graph. ii. Draw the cumulative distribution function for X. iii. Calculate the following: P(X=4) P(X≠5) P(X=1 or X=6) P(X4) E(X) Var(X) sd(X) iv. Consider the random variable Y where the outcome...
Question 1 0/1 point (graded) Which of the following is not a finding of Duflo (2001)? The growth in education levels was higher in places where more schools were built. Younger people were on average more educated than older people. Prior to the building of the schools, the regions where schools were built were similar to the regions where the school's weren't built In regions where a lot of schools were built, people were on average less educated prior to...
1. Suppose that random variables X and Y are independent and have the following properties: E(X) = 5, Var(X) = 2, E(Y ) = −2, E(Y 2) = 7. Compute the following. (a) E(X + Y ). (b) Var(2X − 3Y ) (c) E(X2 + 5) (d) The standard deviation of Y . 2. Consider the following data set: �x = {90, 88, 93, 87, 85, 95, 92} (a) Compute x¯. (b) Compute the standard deviation of this set. 3....
(1 point) The following density function describes a random variable X F(x) = m if 0 and if 8<x< 16. Draw a graph of the density function and then use it to find the probabilities below A. Find the probability that X lies between 1 and 6. Probability B. Find the probability that X lies between 5 and 10. Probability C. Find the probability that X is less than 9. Probability D. Find the probability that X is greater than...