**Problem 4.** Let \( f_X(x) \) be the probability density function of \( X \), which is given by\[f_X(x) = \begin{cases} ce^{-2x}, & x \geq 2 \\0, & \text{otherwise}\end{cases}\](a) Find the value of \( c \) to make \( f_X \) a valid probability density function.(b) Calculate the cumulative distribution function (c.d.f.) of \( X \).(c) Calculate \( \mathbb{P}(12 < X \leq 25) \) using the c.d.f. from part (b). You do not need to simplify your answer.

Let fX(x) be the probability density function of X , which is given by fX(x) = ce-2x ,x≥20,…

Answered: Problem 4. Let fx(x) be the probability…

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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6. Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-x, o0) is a function f such that f(r) 20 and (2) = = 1. (a) Determine which of the following functions are probability density functions on the (-x0, 00). fr-1 00 (b) We can also use probability density functions to find the erpected value of the outcomes of the event - if we repeated a probability experiment many times, the expected value will equal the average of the outcomes of the experiment. (e.g. rf(x) dr yields the expected value for a density f(r) with domain on the real numbers.) Find the expected value for one of the valid probability densities above.
Q.2 Let X has the following probability density function: fx(x) = a e-ax;x > 0 Find moment generating function and then using it find mean and variance. End of Quiz
1. The length of time required by students to complete a one-hour exam is a random variable, X, with the probability density function given by f(x) = [cx²+x, 0≤x≤1 10, elsewhere (a) Find c. (b) Find F(x) (c) Use F(x) to find the probability that randomly selected student will finish in less than 45 minutes. (d) Find the probability that randomly selected student needs at least 15 minutes and will finish in less than 30 minutes. (e) Find μ and o.
can you please expand and explainn this problem
Suppose lifetime of a particular type of old mobile, ?, can be modelled by the probability density function............ Answer follow image:
Why is P(X = c) = 0 for any number c in the domain of a probability density function?
2..You are given fT(30)(t) = t/1250 0≤t<50 0 o.w. a) Find the probability that (30) dies between ages 40 and 45. b) Find the probability that (60) dies between ages 65 and 85. c) Define the cumulative distribution function of T (45). d) Define the force of mortality of T (50).
1. Suppose that for a certain life the probability density function is x (*) 1+x ,x >0 X. Find (i) the survival function ofx (ii) the probability that the life aged 25 will die within next 15 years. (iii) the probability that the life aged 42 will die between 55 and 62.
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.
Suppose that the probability density function of a random variable X is as follows: f(x)= cx, for0<x<4; 0, otherwise. (a) Find c.(b) Find the cumulative distribution function F and sketch it.

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