Exercise 2. Let consider a normally distributed random variable Z with mean 0 and variance 1....
The random variable Z has a Normal distribution with mean 0 and variance 1. Show that the expectation of Z given that a < Z < b is o(a) – °(6) 0(b) – (a)' where Ø denotes the cumulative distribution function for Z.
Let X be a random variable with CDF z<0 G()=/2 0 <IS2 z>2 1 Suppose Y = X2 is another random variable, find (a) P(1/2 X 3/2), (b) P(1s X< 2) (c) P(Y X) (d) P(X 2Y). (f) If Z VX, find the CDF of Z. (d) P(X+Y 3/4)
Exercise 4 (Continuous Probability) For this exercise, consider a random variable X which is normally distributed with a mean of 120 and a standard deviation of 15. That is, x-.. N (μ = 120, σ. 225) (a) Calculate P(X<95) (b) Calculate P(X > 140) c) Calculate P(95<X<120 (d) Find q such that P(X<)-0.05 (e) Find q such that P(X>) 0.10
Assume that z-scores are normally distributed with a mean of O and a standard deviation of 1. If P(0 < z < a) = 0.4857, find a. a = (Round to two decimal places.)
Let Z be a standard normal random variable. Use the calculator provided, or this table, to determine the value of c. P(-csz<c)=0.9426 Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places. x 3 ? Let Z be a standard normal random variable. Use the calculator provided, or this table, to determine the value of c. P(0.55 <<c) -0.2624 Carry your intermediate computations to at least four decimal places. Round your answer to...
Exercise 3.38. Let the random variable Z have probability density function 24 fz(z) = -1 <z<1 otherwise. (a) Calculate E[Z]. (b) Calculate P(0 <Z<į). (c) Calculate P(Z < į 12 > 0). (d) Calculate all the moments E[Z"] for n= 1,2,3,... Your answer will be a formula that contains n.
CI Assume the random variable x is normally distributed with mean probability 89 and standard deviation ơ 4 Find the indicated Px 83) P(x < 83) (Round to four decimal places as needed.) Enter your answer in the answer box imal p O Type here to search 图自3 e )
SELF ASSESSMENT 1 X is a normally distributed random variable with mean 57 and standard deviation 6. Find the probability indicated P(X <59.5) а. P(X < 46.2) b. P(X> 52.2 С. d. P(X> 70) X is a normally distributed random variable with mean 500 and standard deviation 25 Find the probability indicated. а. Р(X < 400) b. P(466 < X <625) Р(X > С. Р(Х > 400)
(10pts) 2. Assume X is normally distributed with a mean of 5 and variance of 16. Determine the value of x that solves each of the following: P(x < X < 9) = 0.2 b) P(-x < X-5<x) = 0.99
Problem 4. Let X be normally distributed with mean 1 and variance 2.2. (a) Find P0.5 < X < 2). (b) Find 95th percentile of X.