Consider you go to a COVID vaccination centre to getyourself vaccinated. Let the random variable X denotes the time that you have to wait in the queue until it is your turn for vaccination. The probability that there is no queue and you arevaccinated immediately as soon as you reach the centre is 1/4.The probability that there is queue and you have to wait forsome time is 3/4 and random variable X can be modelled as an exponential random variable with parameter (λ = 1/3). (i) Find the CDF of the random variable X. (ii) Pictorially represent CDF of random variable X. What do you infer from the CDF plot? (iii) Find P(0 < X ≤ 1) and P(0 ≤ X ≤ 1) (Note: The CDF of an exponential distribution is given by P(X≤x) = 1-?^-x*? )

Consider you go to a COVID vaccination centre to getyourself vaccinated. Let the random variable X denotes the time that you have to wait in the queue until it is your turn for vaccination. The probability that there is no queue and you arevaccinated immediately as soon as you reach the centre is 1/4.The probability that there is queue and you have to wait forsome time is 3/4 and random variable X can be modelled as an exponential random variable with parameter (λ = 1/3). (i) Find the CDF of the random variable X. (ii) Pictorially represent CDF of random variable X. What do you infer from the CDF plot? (iii) Find P(0 < X ≤ 1) and P(0 ≤ X ≤ 1) (Note: The CDF of an exponential distribution is given by P(X≤x) = 1-?^-x*? )

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Description: Consider you go to a COVID vaccination centre to getyourself vaccinated. Let the random variable X denotes the time that you have to wait in the queue until it is your turn for vaccination. The probability that there is no queue and you arevaccinated

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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