The continuous random variable X has a probability density function (pdf) given byfor 0≤x≤2otherwisef(x) =[1-0Part(a) Two independent observations of X are taken. Find the probability correct to 2 decimaplaces that one is less than and the other is greater than 0.25Part(b) Find E(√X), correct to 2 decimal places. 0.75Part(c) Find E(X), correct to 2 decimal places.Part(d) Find Var(X), correct to 2 decimal places. 0.22Part(e) Find P(X > 1). Give your answer as a decimal, correct to 2 decimal places. 0.56Part(f) Find the median of X, correct to 2 decimal places. 0.59

Given,the continuous random variable has a probability density function (pdf) given by part(a)Two…

Answered: The continuous random variable X has a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A probability density curve is described by 2 line segments. The first connects (0, 1/7) and (3.5. 1/7), and the other connects (3.5, 1/7) to the x-axis. Part A: Sketch the probability density curve as described. (Be sure to label all values) Part B: Determine the x-value where the second segment crosses the x-axis. Part C: Determine P(X 0.05). Part E: Determine the median x-value of this distribution.
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A continous random variable has density function f(x)=(3x?)/(63) for Osxse, for some 0>0, and zero otherwise. What is the ratio of the mode to the median for this distribution? A. 2(1/3) B. 0/(21/3) O C.e D. 2(-1/3)
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Suppose a college professor never finishes her lecture before the end of the class period, and always finishes within five minutes after the class period is supposed to end. Let X = time that elapses between the end of the class period and the actual end of the lecture. Suppose the pdf of X is: (image) Find the value of k that makes f(x) a legitimate probability density function, and use that value of k to find the probability that the lecture ends less than 3 minutes after the class period is supposed to end.

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