which we can replace them to polar coordinate Thus Mean By symmetry if g(x) is odd function g-x=-g(x) then -abgxdx=0 Variance Notation CDF is standard Normal CDF by symmetric ‚CDF ‚ ‚ All the odd moment of standard normal are zero. However‚ even moment is not easy to calculate by integral (Symmetry) Then we say Most of Statistics books will write the pdf then explain the mean and variance but it is not intuitive. Standardization Find PDF of CDF: The
Free Probability theory Normal distribution Variance
and what he saw a dead body on the floor and that was his wife. It was witching hour on a dark moonless night. He was holding his wife body in his arms‚ kissing and crying. Suddenly‚ he heard their voices downstairs again. He stopped crying for a moment. He didn’t know that was his last day of his life. The phone rang once again and answered itself saying” remembered Oct 4th at 2 am”. John knew that day and time very well because he accidentally murdered a married couple on this day. He and his wife
Premium Marriage Camping 2006 singles
baked cookies filled the air‚ as the jolly music played in the background. People are wearing colourfully knitted scarfs and sweaters. The golden sun was always shining in the clear blue sky. Those were the days I will never forget. That special moment when nana pulled out the golden‚ crispy turkey is when you know it’s Christmas time. The lit-up streets were full of dancing‚ bright Santa’s. Every house had flickering‚ blinding lights that made every minute the most exciting yet. There is always
Free Present Time Debut albums
Normal Distribution:- A continuous random variable X is a normal distribution with the parameters mean and variance then the probability function can be written as f(x) = - < x < ‚ - < μ < ‚ σ > 0. When σ2 = 1‚ μ = 0 is called as standard normal. Normal distribution problems and solutions – Formulas: X < μ = 0.5 – Z X > μ = 0.5 + Z X = μ = 0.5 where‚ μ = mean σ = standard deviation X = normal random variable Normal Distribution Problems and Solutions – Example
Premium Normal distribution Standard deviation Random variable
Mean of a log normal random variable: Theorem 1: Suppose Y = ln X is a normal distribution with mean m and variance v‚ then X has mean exp( m + v /2 ) Proof: The density function of Y= ln X Therefore the density function of X is given by Using the change of variable x = exp(y)‚ dx = exp(y) dy‚ We have = Note that the integral inside is just the density function of a normal random variable with mean (m-v) and variance v. By definition‚ the integral evaluates to be 1. Proof of Black Scholes
Premium Normal distribution Standard deviation Variance
ROP based on Normal Distribution of LT demand -Example No. 1 Example : Suppose that the manager of a construction supply house determined from historical records that demand for sand during leadtime averages 50 tons. In addition‚ suppose the manager determined that the demand during leadtime could be described by a normal distribution that has a mean of 50 tons and a standard deviation of 5 tons. Answer the following questions‚ assuming that the manager is willing to accept a stockout risk of no
Premium Normal distribution Variance Standard deviation
Problem Sheet - I 1. Researcher conducted by a tobacco company indicates that the relative frequency distribution of tar content of its newly developed low-tar cigarette has a mean equal to 3.9 milligrams of tar per cigarette and a standard deviation equal to 1.0 milligram. Suppose a sample of 100 low-tar cigarettes is randomly selected from a day’s production and the tar content is measured in each. Assuming that the tobacco company’s claim is true‚ what is the probability that the mean
Premium Standard deviation Normal distribution Probability theory
13. Variance and Standard Deviation (expected). Using the data from problem 13‚ calculate the variance and standard deviation of the three investments‚ stock‚ corporate bond‚ and government bond. If the estimates for both the probabilities of the economy and the returns in each state of the economy are correct‚ which investment would you choose considering both risk and return? Why? ANSWER Variance of Stock = 0.10 x (0.25 – 0.033)2 + 0.15 x (0.12 – 0.033)2 + 0.50 x (0.04 – 0.033)2 + 0
Premium Variance Probability theory Standard deviation
A population of measurements is approximately normally distributed with mean of 25 and a variance of 9. Find the probability that a measurement selected at random will be between 19 and 31. Solution: The values 19 and 31 must be transformed into the corresponding z values and then the area between the two z values found. Using the transformation formula from X to z (where µ = 25 and σ √9 = 3)‚ we have z19 = (19 – 25) / 3 = -2 and z31 = (31 - 25) / 3 = +2 From the area between z =±2 is 2(0
Premium Normal distribution Standard deviation Variance
STAT11-111 Business Statistics WEEK 3 and WEEK 4: WORKSHOPS ______________________________________________ This workshop is to be completed during Week 3 and Week 4 workshops and will depend on how quickly we get through the lecture material. Part A: Week 3 Exercise 4.2‚ Exercise 4.4. Exercise 4.5‚ Exercise 4.6‚ Exercise 4.7. Your tutor will discuss these 3 questions with you in the class. Exercise 4.8‚ Exercise 4.9. Exercise 4.10‚ Exercise 4.12‚ Exercise 4.14. Exercise 4.15‚ Exercise
Premium Variance Probability theory Random variable