(a) Explanation Given info: The random variable X has an exponential distribution with θ = 2.5 . Calculation: Exponential Distribution: A random variable X is said to follow Exponential distribution if the density function of X is, f ( x ) = 1 θ e − x θ , ( x > 0 , θ > 0 ) . Where the mean is μ = θ and the standard deviation is σ = θ . Here, θ = 2.5 . P ( X ≤ 4 ) = 1 − P ( X > 4 ) . As X is a continuous random variable, P ( X > 4 ) = P ( X ≥ 4 ) (b) To determine To find: P ( X > 5 ) . (c) To determine To find: P ( X ≤ 2 ) . (d) To determine To find: P ( X > 3 ) .

Statistics for Business and Economics (13th Edition)

13th Edition

ISBN: 9780134506593

Author: James T. McClave, P. George Benson, Terry Sincich

Publisher: PEARSON

See similar textbooks

Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could co…

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a…

Videos

Question

Chapter 4.8, Problem 4.136LM

(a)

To determine

To find: P(X≤4) .

(b)

To determine

To find: P(X>5) .

(c)

To determine

To find: P(X≤2) .

(d)

To determine

To find: P(X>3) .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.8, Problem 4.135LM

Chapter 4.8, Problem 4.137LM

Students have asked these similar questions

6. Let, for p = (0, 1), and xe R. X be a random variable defined as follows: P(X=-x) = P(X = x)=p. P(X=0)= 1-2p. Show that there is equality in Chebyshev's inequality for X. This means that Chebyshev's inequality, in spite of being rather crude, cannot be improved without additional assumptions.

4. Prove that, for any random variable X, the minimum of EIX-al is attained for a = med (X).

8. Recall, from Sect. 2.16.4, the likelihood ratio statistic, Ln, which was defined as a product of independent, identically distributed random variables with mean 1 (under the so-called null hypothesis), and the, sometimes more convenient, log-likelihood, log L, which was a sum of independent, identically distributed random variables, which, however, do not have mean log 1 = 0. (a) Verify that the last claim is correct, by proving the more general statement, namely that, if Y is a non-negative random variable with finite mean, then E(log Y) log(EY). (b) Prove that, in fact, there is strict inequality: E(log Y) < log(EY), unless Y is degenerate. (c) Review the proof of Jensen's inequality, Theorem 5.1. Generalize with a glimpse on (b).

Chapter 4 Solutions

Statistics for Business and Economics (13th Edition)

Ch. 4.1 - Types of random variables. Which of the following...Ch. 4.1 - Types of finance random variables. Security...Ch. 4.1 - NHTSA crash tests. Refer to the National Highway...Ch. 4.1 - Customers in line at a Subway shop. The number of...Ch. 4.1 - Executive pay. Refer to Glassdoor Economic...Ch. 4.1 - Banking. Give an example of a discrete random...Ch. 4.1 - Economics. Give an example of a continuous random...Ch. 4.1 - Hotel management. Give an example of a discrete...Ch. 4.1 - Retailing. Give two examples of discrete random...Ch. 4.1 - Stock market. Give an example of a continuous...

Knowledge Booster

$Statistics$

Learn more about

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

P ( X ≤ 4 ) .

Solution Summary: The author explains that the random variable X has an exponential distribution with theta =2.5.

Concept explainers

Videos

To find: P(X≤4) .

To find: P(X>5) .

To find: P(X≤2) .

To find: P(X>3) .

Want to see the full answer?

Chapter 4 Solutions