Consider the following exponential probability density function.\[ f(x) = \frac{1}{5} e^{-\frac{x}{5}} \quad \text{for} \quad x \geq 0 \]a. Which of the following is the formula for \( P(x \leq x_0) \)?1. \( P(x \leq x_0) = e^{-\frac{x_0}{5}} \)2. \( P(x \leq x_0) = 1 - e^{-\frac{x_0}{5}} \)3. \( P(x \leq x_0) = 1 - e^{-x_0} \)- Select your answer -b. Find \( P(x \leq 1) \) (to 4 decimals).- Input box -c. Find \( P(x \geq 4) \) (to 4 decimals).- Input box -d. Find \( P(x \leq 5) \) (to 4 decimals).- Input box -e. Find \( P(1 \leq x < 5) \) (to 4 decimals).- Input box -

As per our guidelines we are suppose to answer three sub parts. Given,f(x)=15 e-x5 ; x≥00…

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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The cumulative distribution function of a random variable X is defined by the equation: (in the picture)a. Determine the probability density function of the random variable X b. Determine the probability random variable x from ½ to 1 c. Is the probability density function a valid PDF?
Given the following probability density function: f(x) = 4 exp(1 – 4x) for x > 0.25 Find the corresponding distribution function F(x) for x > 0.25 O - exp( 1 - 4x) O 1 O 1- exp( 1 - 4x )
(c) At a bus stop, there are two buses available (bus numbers 1 and 2). For i = 1,2, the waiting time until bus i arrives is denoted by T;, with T independent of T2, and T; has density function fr. (t) = X, exp(-1;t), t>0.
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Consider the following exponential probability density function. 1 -x/4 f(x) = -e (a) Write the formula for P(x ≤ xo). for x ≥ 0 (b) Find P(x ≤ 2). (Round your answer to four decimal places.) (c) Find P(x ≥ 4). (Round your answer to four decimal places.) 0.3679 (d) Find P(x ≤ 5). (Round your answer to four decimal places.) (e) Find P(2 ≤ x ≤ 5). (Round your answer to four decimal places.)
The exponential distribution is a probability distribution for non-negative real numbers. It is often used to model waiting or survival times. The version that we will look at has a probability density function of the form p(y|v) = exp(-e¯ºy — v) (1) where y R+, i.e., y can take on the values of non-negative real numbers. In this form it has one parameter: a log-scale parameter v. If a random variable follows an exponential distribution with log-scale v we say that Y~ Exp(v). If Y~ Exp(v), then E [Y] =e" and V [Y] = e²v. 1. Produce a plot of the exponential probability density function (1) for the values y E (0, 10), for v = 1, v = 0.5 and v= 2. Ensure the graph is readable, the axis are labeled appropriately and a legend is included. ta il 2. Imagine we are given a sample of n observations y = (y₁,..., yn). Write down the joint proba- bility of this sample of data, under the assumption that it came from an exponential distribution with log-scale parameter v (i.e., write down the…
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For a given probability density function below, solve for "c" so that it becomes a valid pdf. {i x > 1 f (x) = x3 x < 1 5 O 6 O 4 none of these O 3
The probability density function of X is given by f(x) = 6 – 2x, 2
Recall that the exponential probability density function is defined as 1 f(x) = — - e-2/A. е Suppose that the lifetime in hours of a certain lightbulb is exponential distributed with λ = 3000. Find the probability that a given lightbulb will last more than 7300 hours. P(X> 7300)

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