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.
Alex decides to sell his old guitar, and sequentially receives bids from potential buyers. The minimum price that he will accept to sell his guitar for is £500. Let {Xn, n ≥ 0} denote the sequence of independent and identically distributed bids that Alex receives, and assume that each Xn has the following probability density functionfX(x) = (1/400)e-x/400 for x ≥ 0. Let N denote the number of bids that Alex obtains before selling his guitar i.e., Alex sells his laptop to the Nth bid. Showing your full working, (a) find E[N]. (b) find E[XN].
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Suppose a random variable X has a probability density function given by O elsewhere f (x) = kx (1 − x) 0 ≤ x ≤ 1 0 elsewhere 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) d. Find P (0.8 ≤ x))
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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).
Let fx(x) be the probability density function of the random variable X. 3 22-4< e< 4; Ka) - f(z) = { 128 otherwise. Determine the E{X}. [The answer should be a number rounded to five decimal places, don't use symbols such as %

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