Normal distribution and discriminant functions
Matlab
Write a procedure to calculate the Mahalanobis distance between the mean µ and an arbitrary point x, given the covariance matrix Σ.
>mu=[5 3 7]'
>x=[1 2 3]'
.>sigma=[4 -1 0;-1 4 2;0 2 9]
>d=sqrt((x-mu)'*inv(sigma)*(x-mu))
Normal distribution and discriminant functions Matlab Write a procedure to calculate the Mahalanobis distance between the...
Pattern Recognition Normal distribution and discriminant functions Matlab - Write a procedure to generate random samples according to a normal distribution N(µ, Σ) in d dimensions
Example 1. Assume that the random variable X follows the Normal distribution with mean 75 and standard deviation 10. Use Python to(a) Compute P(65 < X < 85) and interpret the findings(b) Compute P(55 < X < 95) and interpret the findings(c) Compute P(X > 100) and interpret the findingsExample 2. Assume that the random variable X follows the Normal distribution with mean µ and standard deviation σ. Compute (a) P(µ − σ < X < µ + σ) (b) P(µ −...
Consider two sample means distributions corresponding to the same x distribution. The first sample mean distribution is based on samples of size n=100 and the second is based on sample of size n=225.Which sample mean distribution has the smaller standard error? Explain. What percentage of the area lies under the standard normal curve (a) to the left of the µ? (b) between µ – σ and µ + σ? (c) between µ - 3 σ and µ + 3 σ?
matlab code please
MATLab 1. Using MatLab, write a program to calculate the range of x values for a Gaussian distribution assuming an arbitrary confidence (e.g. 85%) Suppose that there are 3000 air molecules in an otherwise empty room. What is the probability that exactly 1000 of them are in the front third of the room at any instant? What is the probability that 1001 of them are in the front of the room? What is the probability that there...
Let X have a normal distribution with mean µ = 30 and standard deviation σ = 10. Calculate P(X > 40), and round your answer to two decimal places.
Given a normal distribution with µ = 100 and σ = 10, if you select a sample of n = 25, what is the probability that ? is Between 95 and 97.5? (a) 0.9878 (b) 0.0994 (c) 0.9500 (d) 0.8616 8. Given a normal distribution with µ = 100 and σ = 10, if you select a sample of n = 25, there is a 64.8% chance that ? is above what value? [Hint find A such that P(?� >A)=0.648]...
2. Suppose that you can draw independent samples (U,, U2,U. from uniform distribution on [0,1]. (a) Suggest a method to generate a standard normal random variable using (U, U2,Us...) Justify your answer. b) How can you generate a bivariate standard normal random variable? (Note that a bivariate standard normal distribution is a 2-dimensional normal with zero mean and identity covariance matrix.) (c) What can you suggest if you want to generate correlated normal random variables with covariance matrix Σ= of...
A population forms a normal distribution with a mean of µ = 120 and a standard deviation of σ = 14. If two scores were selected from this population, how much distance would you expect, on average, between the second score and the population mean? A sample of n = 20 scores from this population has a mean of M = 90, do you think this sample is relative typical or extreme to the population? Explain. With a large standard...
Suppose the random variable X follows a normal distribution with mean µ = 84 and standard deviation σ = 20. Calculate each of the following: P(X > 100) P(80 < X < 144) P(124 < X < 160) P(X < 50) P(X > X*) = .0062. What is the value of X*?
Given that X is a continuous random variable that has a uniform probability distribution, and 0 < X < 8: a. Calculate P(X < 4) (to 3 significant digits). P(X < 4)= b. Determine the mean (µ) and standard deviation (σ) of the distribution (to 3 significant digits). µ = σ =