USING R AND RSTUDIO PLEASE PROVIDE EXPLANATION AS WELL, THANK YOU(:
Part 2: Normal distribution z-N(0,1):f(x) :v2ne- # The function dnorm returns the height of the n...
PLEASE ANSWER THE HIGHLIGHTED PARTS ONLY. REALLY NEED PART G. Suppose X has a normal distribution with mean -3 and standard deviation 7. The pnorm(), dnorm() and qnorm() functions should be useful in the following. a) What is the expected value of 5X + 15? b) What is the variance of 5X + 15? c) Calculate the probability X >0. d) Calculate the probability that X < -10 e) Calculate the probability that 1 < X < 10. f) If...
Now let's try a normal distribution. The first plot will be easy, but the second will be more difficult to do, so follow the instructions carefully. First we'll plot a standard normal, then we'll see what happens if you change the parameters. x <- seq (-3.291, 3.291, length.out=100) gives us 100 equally spaced values of x between -3.291 and 3.291. “seq” let's us generate a sequence of numbers, and “length.out” tells us how many numbers we want in the sequence....
(ii) Suppose X N(0,1) has the standard normal distribution. Find the probability distribution function ofY - 2
Answer 5 and 6, using R programming code: 5. We have seen the following functions dnorm pnorm qnorm normal probability density function normal cumulative distribution function normal quantile function a. Let X have a normal distribution with mean 100 and variance 100. Find the 90th percentile of X by calling the function qnorm in two ways: (i) specify the arguments by position, and (ii) specify the arguments by complete names. b. Find P(X > 90) using the function pnorm in...
(a) (2 pt) If X is uniform on (0,1), then for what function f is f(x) exponential with parameter 1? (b) (3 pts) If X,Y are independent standard normal random variables N(0,1), what is the density of X -Y?
Assume that 2 and Z, are two independent random variables that follow the standard normal distribution N(0,1), so that each of them has the density - . - < < . Let X = 22 + 2 Z2, Y = 22 - Z2, S = x2 +Y, and R = xy (e) From (c), please find the densities of X? and Y? (f) From (d) and (e), please find the density of X2 +Y? (=S). (g) From (e), please find...
This is Probability and Statistics in Engineering and Science Please show your work! especially for part B A Poisson distribution with λ=2 X~Pois(2) A binomial distribution with n=10 and π=0.45. X~binom(10,0.45) Question 4. An inequality developed by Russian mathematician Chebyshev gives the minimum percentage of values in ANY sample that can be found within some number (k21) standard deviations from the mean. Let P be the percentage of values within k standard deviations of the mean value. Chebyshev's inequality states...
1. True or False: (1pt each) (T) (F) If a distribution is normal, then it is not possible to randomly select a value that is more than 4 standard deviations from the mean. (T) (F) Normal distribution is a discreet probability distribution for a random variable. (T) (F) If the variable follows a binomial distribution, then about 68 % of the variables are within 1 SD of the mean, about 95% of the variables are within +2 SD of the...
Suppose X has a standard normal distribution. The pnorm(), norm(), and qnorm() functions should be useful in the following. Remember, if X has a standard normal distribution then E(X) = 0 and Var(x)=1. a) What is the expected value of Xt1 ? b) What is the variance of X c) What is the expected value of xo? d) Using R, calculate the probability X > .83) e) Using R, calculate the probability that -0.2 <x< 1.1 f) Using R, calculate...
A normal distribution is fully determined if we know its: Select one: a. Probability density function. b. All the given answers. c. Cumulative distribution function. d. Mean and standard deviation.