Problem 1 (15%): Find the following probabilities for two normal random variables Z = N(0,1) and...
4.28 If Z ~ N(0,1), find the following probabilities: a. P(Z <1.38) b. P(Z > 2.14) c. P(-1.27 <Z<-0.48)
(1 point) Find the following probabilities for the standard normal random variable z. (a) P(-0.81 <<0.42) (b) P(-1.14 <z < 0.5) (c) P(Z < 0.69) a (d) P(Z > -0.6)
Standart Normal Probabilities Let Z be a standard normal random variable. Calculate the following probabilities using the calculator provided. Round your responses to at least three decimal places. P(Z >-2.11) P(Z 1.82) = P (-048<Z < 205) Clear Undo Help Next>> Explain
Suppose Z is a standard normal random variable. (See problem.) If P(-z<z<z) 0.796, find Question 1 Find P(-2.46 <Z<-0.98) Question 2
9. Let X and Y be two random variables. Suppose that σ = 4, and σ -9. If we know that the two random variables Z-2X?Y and W = X + Y are independent, find Cov(X, Y) and ρ(X,Y). 10. Let X and Y be bivariate normal random variables with parameters μェー0, σ, 1,Hy- 1, ơv = 2, and ρ = _ .5. Find P(X + 2Y < 3) . Find Cov(X-Y, X + 2Y) 11. Let X and Y...
3. Let Z be a continuous random variable with Z-N(0,1). (a) Find the value of P(Z <-0.47). (b) Find the value of P(Z < 2.00). Note denotes the absolute value function. (c) Find b such that P(Z > b) = 0.9382. (d) Find the 27th percentile. (e) Find the value of the critical value 20.05-
1. Given that z is a standard normal random variable, compute the following probabilities. a. P(Z < 1.38) b. P(z 2 1.32) c. P(-1.23 Sz5 1.23)
For two bivariate normal random variables X~N(0,1), Y~N(5,1), and CovX,Y=-0.5, answer the following questions: Compute P(Y>5|X=1) Compute P(Y>5|X=-1) Explain why the computed probability in b is greater than that in a. Compute P(2X-Y>-3).
Q4) Let X and Y be two independent N(0,1) random variable and 10 ei Find the covariance of Z and W.WE3-Y Q4) Let X and Y be two independent N(0,1) random variable and 10 ei Find the covariance of Z and W.WE3-Y
A) 0.7995 11. If Z is a standard normal variable find the probabilities of a) P(Z <-0.35)- @w B) 0.3982 C) 1.2008 D) p.4013 (2 points) b) P(0.25s Z<1.55) (3 points) c) P(Z > 1.55) (2 points) 12. Assume that X has a normal distribution with mean deviation .5. Find the following probabilities: 15 and the standard a) P(X < 13.50)- 3 points). b) P (13.25 <X < 16.50)- (5 points). B) 0 2706 C0 5412 D) 1.0824 A mountuin...