Let Z be the standard normal random variable.(a) Find the value of the probability density function fx(x) of X = |Z+1| for x = 1.= 2.(b) Find the value of the probability density function fy(v) of Y = e² for y(c) Find E[Y4] (Hint: this problem is closely related to the moment generating function for the normaldistribution.)

Answered: Image /qna-images/answer/254011d0-5d48-491b-a398-8818b5a89a85.jpg

Answered: et Z be the standard normal random…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The data for the joint probability mass function of X and Y (two different measurement systems) aregiven in the table below.a) Calculate the marginal distributions of X and Y and plot them.b) Select one of the Y values from the table and find the conditional probability mass function of X for thatY value you have selected and plot it.c) Show whether X and Y are independent or not.d) Calculate the covariance of (X,Y) i.e. Cov(X,Y).
Why is P(X = c) = 0 for any number c in the domain of a probability density function?
The random variables X and Y have a joint probability density function given by f(x, y) = way, 0 < x < 3 and 1 < y < x, and 0 otherwise.
Tyson Corp. stock has returns of 3%, 18%, -24%, and 28% for the past four years. Based on this information, what is the 99% probability range for any one given year? Select one: Oa 24.5 to 34.3% O b.-61.7 to 74.2% OC.-8.4 to 11.7% Od.-16.4 to 28.9% e. 39.0 to 51.5%
For the probability density function f defined on the random variable x, find (a) the mean of x, (b) the standard deviation of x, and (c) the probability that the random variable x is within one standard deviation of the mean. 1 f(x) = x, [5,9] 28 a) Find the mean. %3D (Round to three decimal places as needed.) b) Find the standard deviation. (Round to three decimal places as needed.) c) Find the probability that the random variable x is within one standard deviation of the mean. The probability is. (Round to three decimal places as needed.)
let x,y be two random variable with joint probability density function -1 0.1 0.2 0.1 0.2 0.1 0.2 1- Find E( x/y-0)
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