Problem 5The random variable X, which denotes the interval between two consecutive events, has the PDF:fx(x) = 4x²e-2x x ≥ 0If we assume that intervals between events are independent, determine the following:(a) The expected value of X.(b) The expected value of the interval between the 11th and 13th events(c) The probability that X ≤ 6.

Given that, The random variable X is the interval between two consecutive events. The pdf is given…

Answered: Problem 5 The random variable X, which…

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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Given the following probability distribution for the number of semesters of Math a (non-Math major) college student will take as they earn their degree: x:number of semesters of Math 1 2 3 4 P(x) 0.25 0.45 0.20 0.10 What is the probability that a randomly selected (non-Math major) college student will have taken exactly 3 semesters of Math? Show how you calculated your result here (type in what you typed on your calculator or computer, etc) Calculation: __________ Now type in your final simplified or rounded answer, if necessary round your answer to four decimal places. P(exactly 3 semesters of Math) = _____________
Problem 1) From previously published studies, the probability that a pine snake hatched in a zoo will survive to maturity is 72%. If five pine snakes are hatched, what is the predicted probability distribution for the number of pine snakes that will survive to maturity? (Find Prob(X=k) for k = 0, 1, 2, 3, 4, and 5.) Carry three decimal places in your calculations. 1. Choose the correct answer for k = 0 а. 0.022 b. 0.020 с. 0.002 d. 0.030 2. Choose the correct answer for k= 1 а. 0.022 b. 0.020 с. 0.002 d. 0.030
Question 3 According to the historical data, 72.9% of the 20-year-olds live until 65 years old. A random sample of size 70 was obtained. Let be the proportion of the sample that live until 65 years old. ) to describe the probability distribution of pand 1. Use the Central Limit Theorem (Select an answer Select an answer np>10 and n(1-p)>10 n(1-p)10 np10 state its parameters and op: (Round the answers to 4 decimal places) p~ Select an answer Select an answer N X² unknown F T B (H₂ 3 op= 2. Find the probability that more than 85% of the sample live until 65 years old. (Round the answer to 4 decimal places)
Please solve (a) & (b) only!
1. Suppose you are a technician, whose repair time on a given job is said to follow an exponential distribution with expected time θ = 3 hours. You have 5 independent jobs lined up (you complete them sequentially, one by one). a. What is the probability of taking exactly 2 hours to finish a given job? b. What is the probability it will take more than 2 hours on a given job? c. You are on a given job and you already have been working for 1 hour. What is the probability it will at least an additional 2 hours to complete this job?
QUESTION 1 Let X be a normal random variable with mean u = 68 and standard deviation o =11. What is the probability that Xwill be (a). more than 79? (b). between 57 and 79? (c), less than 46?
(Don't write handwriting. .)
Question 2: X ~ Geometric(T) distribution with probability function p(x) = P(X = x) = T(1 – 7)"-1 for x = 1, 2, 3, ... Find P(X x).

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