Consider the following exponential probability density function.a. Which of the following is the formula for P(x ≤ xo)?1 P(x ≤ x₁) = e = 722 P(x ≤ x₁) = 1 - e i3 P(x ≤ xo) = 1- e=0Formula #2b. Find P(x ≤ 2) (to 4 decimals).c. Find P(x > 4) (to 4 decimals).×d. Find P(x ≤ 6) (to 4 decimals).e. Find P(2 ≤ x ≤ 6) (to 4 decimals).f(x) = 1⁄2 e¯for x>0JL1

The exponential probability density function is given by; f(x)=12e-x2 for x≥0

Answered: Consider the following exponential…

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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You are given the probability distribution function (PDF) of a continuous random variable X is fX(x). Let Y be a continuous random variable such that Y = aX + b, where a and b are non-zero real constants.1. Find the PDF of Y in terms of fX , a, and b.2. Let X be an exponential random variable with parameter λ. When will Yalso be an exponential random variable? 3. Let X be a normal random variable with mean μ and variance σ2 . Whenwill Y also be a normal random variable?
The line of best fit through a set of data is ý = 38.241 – 1.827r According to this equation, what is the predicted value of the dependent variable when the independent variable has value 20? y = Round to 1 decimal place.
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, [2,4] ..... a) Find the mean. (Round to three decimal places as needed.) b) Find the standard deviation. O = (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.)
The following is a probability distribution function for X, with range 0, 1, 2, 3: P(X = 0) = 0.3; P(X = 1) = 0.2; P(X = 2) = 0.3; P(X = 3) = 0.2. Compute E(X). Round your answer to one decimal place.
Consider the following exponential probability density function. a. Which of the following is the formula for P(x ≤ xo)? 1 P(x ≤ xo) = e TO Formula #2 20 2 P(x ≤ xo) = 1-e 3 P(x ≤ xo) = 1-e-20 b. Find P(x ≤ 1) (to 4 decimals). c. Find P(x ≥ 4) (to 4 decimals). 0.3679 d. Find P(x ≤ 6) (to 4 decimals). 0.7769 e. Find P(1 ≤ x ≤ 6) (to 4 decimals), 1 f(x) = = e h for 20
Suppose a random variable X has a probability density function in img.jpg. a. Find the value of k that makes this a probability density function. b. Find P(0.4≤X≤1). c. Find P(X≤0.4|X≤0.8) d. Find F(b) = P(X≤b) and sketch the graph of this function.
.) The probability density function of the random variable X is given by: -{cou Sce-2 for x ≥ 0 otherwise. f(x) = For what value of c is this a legit density function? Find the value for c, then calculate P(X > 2).

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