**Problem Statement:**A random variable $ X $ has an exponential density function given by:\[f(x) = \begin{cases} 0.2e^{-2x} & \text{for } 0 \leq x \\0 & \text{otherwise}\end{cases}\]Find the probability that $ X $ is between 4 and 6 (to three decimal places).

Answered: 17. A random variable X has an…

17. A random variable X has an exponential density function .2x f(x) .2e- = 0 otherwise Find the probability that X is between 4 and 6 (to 3 decimals).

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...

See similar textbooks

Related questions

Q: Suppose a is a random variable best described by a uniform probability that ranges from 21 answers…

A: As per guidelines expert have to answer first question three subparts only since I have done all for…

Q: Suppose that a random sample X is given by a probability density function 2 f(x) = {ß² (B2), 0<x<ß…

Q: 5. The probability density function of the time to failure of an copier (in hours) is -x/1000 f(x):…

A: Given,

Q: 5.1. Let X be a random variable with probability density function f(x) = {€ c (x − ²³2) 2 < x < 4 0…

A: The probability density of X has the form: f(x) = c(x - 3x2)2 < x <40otherwise (a). Find the…

Q: We are given the probability density function of a t-distribution t(µ, 1) (shown in attached image):…

A: Given Pdf

Q: 5. Suppose that the current stock price is 100 $. Its annualized volatility is 25 % and return 15 %…

Q: Let the joint probability density function for X and Y be f(x, y) = 0<r<y<1 otherwise Find the value…

Q: An electronic product with n identical parts connected in parallel cannot function properly only if…

Q: The life of a machine component has X days. The random variable X is defined by the P(X) P(X=x ) = {…

A: Note: " Since you have posted many sub-parts. we will solve the first three sub-parts for you. To…

Q: 3. The random variable r represents the annual rainfall depth in El Paso in inches. Be- tween values…

A: We have given that the random variable x represents the annual rainfall depth in El Paso in inches.…

Q: 9. Let p(x) = 4 T(1 + (2x)²) for 20 (and p(a) = 0 if a <0). (a) Show that p is a probability density…

A: 9. Given that p(x)=4π1+2x2 for x≥0. First, we have to show that p is a probability density…

Q: 1. Waiting time. Let the time waiting in line, in minutes, be described by the random variable X…

Q: (4) Find the conditional probability that the watch has an operational lifetime in excess of 5 years…

Q: Given the probability density function f(x) = }x over [1, 3], find each of the following. 15. E(x)…

A: Given the probability density function fx=14x ;0≤x≤3 15. We need to find E(X). Formula for E(X)…

Q: Let the random variable Y possess a uniform distribution on the interval (0,1). Use the…

A: Given That Y~U(0, 1) with PDF as:We have to PDF of by using the method of transformation and…

Q: Q4. A random variable X takes values between-2 and 3 with a probability density function 15 64 + cx,…

Q: The Probability density function of the continuous random variable X is given as if x 2k fx(x) =…

A: Given, The pdf of X is fXx=kx2 , if x≥k0 , otherwise

Q: 8. A random variable has a probability density function given by (4 x - 1 f(x) = 0 ≤ x ≤ 1, ≤ 2, 1 ≤…

A: The probability density function of the random variable is given by,

Q: a) On a particular trading day, you are going to buy shares of the stock that is the cheapest. Find…

Q: ilometers from home (along the road) is a. What is the probability that you dropped it within 1…

A: Solution

Q: QUESTION 3 Suppose L is a lognormal random variable with parameters 0 and 1, that is. L- exp(2)…

A: The expected value of a log normal distribution with parameters μ=0,σ=1 is given by:…

Q: The distribution of salaries (in £10,000s per annum) in the building industry is represented by a…

A: 1) It is needed to find the value of C.

Q: 5. Two fair dice are rolled. Let X be the maximum of the results of two dice. (a) Probability Mass…

Q: Let the probability density function of the random variable X be given as (pdf). Event A = |X-b…

Q: Let 0 be a parameter. Show that the family of functions fo(x) = x >0 à probability density function.…

A: 4. Condition for probability density function ∫f(x)=1. consider, ∫0∞f(x)dx=∫0∞θe-θxx2dx…

Q: Q1 Let X be the number of minutes that it takes a random selected student to solve a mathematical…

Q: * The waiting time T (in hours) between each SMS you receive is random with the density function.…

Q: 16. For the probability density function shown, what is the probability of the random variable æ…

A: To find: The probability of the random variable x being less than 1/3 ?

Q: The probability density function of a random variable is kVx+ – 1 f(x) - if 1 s x< 2

A: Hello! As you have posted 3 different questions, we are answering the first question. In case you…

Q: 5. Let 0 and a be parameters. Show that the family of functions fo,a(x) = x > 0 (r + 0)a+1' is a…

Question

**Problem Statement:**

A random variable $ X $ has an exponential density function given by:

\[
f(x) =
\begin{cases}
0.2e^{-2x} & \text{for } 0 \leq x \\
0 & \text{otherwise}
\end{cases}
\]

Find the probability that $ X $ is between 4 and 6 (to three decimal places).

Expert Solution

Step 1

The probability that X is between 4 and 6 is,

$\begin{array}{rcl} P (4 \leq x < 6) & = & \int_{4}^{6} f (x) d x \\ = & \int_{4}^{6} 0.2 e^{- 0.2 x} d x \\ = & 0.2 \int_{4}^{6} e^{- 0.2 x} d x \\ = & 0.2 {[- \frac{e^{- 0.2 x}}{0.2}]}_{4}^{6} \\ = & - [e^{- 0.2 \times 6} - e^{- 0.2 \times 4}] \\ = & e^{- 0.8} - e^{- 1.2} \\ = & 0.148 \end{array}$

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Multivariate Distributions and Functions of Random Variables$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

Defects occur along the length of cable at an average of 5 defects per 4,000 feet. Assume that the probability of k defects int feet of cable is given by the probability mass function: e -(5t/ 4000) ( 5 t/ 4,000 ) k P(k defects ) = k ! for k = 0, 1, 2, .. Find the probability that a .... 3,200 foot cable will have а. at most three defects b. at least four defects С. between 1 to 5 (inclusive) defects
The normal probability density function g(x) = ov2n Where u = mean, o = standard deviation, n = 3.14159, e 2.71828 Let's study a special case where u = 0 and o = 1, which indicates a standard normal probability density function. For simplicity, we scale the function so as to remove the factor 1/(ov2n). Now, we have a new function f(x) f(x) = e (a) Find f'(x) and show the intervals of increase or decrease for f. (b) Find the extreme value of f. (c) Find the intervals of concavity and the inflection points. (d) Sketch the graph of f and point out the extremum value and inflection points.
do al otherwise not
1
ansewr D and E only
umple 27: If a random variable has the probability density function k(x? – 1),-1