Chapters: Normal and Exponential random variables.Q: There exist naturally occurring random variables thatare neither discrete nor continuous. Suppose a group ofpeople is waiting for one more person to arrive beforestarting a meeting. Suppose that the arrival time of theperson is exponential with mean 4 minutes, and thatthe meeting will start either when the person arrives orafter 5 minutes, whichever comes first. Let X denotethe length of time the group waits before starting themeeting.- a. Find P(0

Answered: Image /qna-images/answer/d639d69f-3092-430a-981b-feaf0ca01fd0.jpg

Answered: :There exist naturally occurring random…

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

Similar questions

Consider a random walk on {0, ..., k}, which moves left and right with respec- tive probabilities q and p. If the walk is at 0 it transitions to 1 on the next step. If the walk is at k it transitions to k – 1 on the next step. This is called random walk with reflecting boundaries. Assume that k = 3, q = 1/4, p = 3/4, and the initial distribution is uniform. For the following, use technology if needed. 1p. (a) Exhibit the transition matrix.
Suppose #7 buses arrive at a bus stop according to a Poisson process with an average of 5 buses per hour. (i.e. X = 5/hr. So 0=hr. or 12 min.) Find the probability (a) you have to wait longer than 15 minutes for a bus (b) you have to wait more than 15 minutes longer, having already been waiting for 6 minutes.
. A twig of length 1 is broken into two pieces at random, and one piece is thrown away. Theremaining piece is then also broken at random, and one piece of that is thrown away. Let X be thelength of the twig that remains. What is the probability that X > 1/2?
Suppose that customers arrive in a small store according to a Poisson process with an average rate of 1 customer every 5 minutes. Find the probability that, on a given day, the very first customer shows up after 10 minutes.
6.15) Consider a sequence of independent trials, with each trial being a success with probability p. Given that the kth success occurs on trial n, show that all possible outcomes of the first n 1 trials that consist of k 1 successes and n -k failures are equally likely. -
2. Let the random variable X denote a natural number selected at random from 1 to 25 inclusive. Find E[X). а. 12 ь. 12.5 c. 13 d. 13.5 е. 14
2. Suppose alpha particle emissions of carbon-14 are counted by a Geiger counter each second. The emissions follow a Poisson process with the mean of 16 particles per second. Let W equal the time in seconds before the seventh particle is counted. a) Give the distribution of W. b) Find P(W ≤ 0.5).
Suppose that customers arrive at a diner at a Poisson rate of A = 3 per hour. What is the probability that exactly 6 customers arrive between 1PM and 3PM and that exactly 4 customers arrive between 4PM and 5PM? Hint: You're dealing with two discrete rv's, in this case. (Answer as a decimal number, and round to 3 decimal places).
6. Let X₁ be a r.v. having a Poisson distribution with mean 4, X₂be a random variable having a Poisson distribution with mean 2. What is the distribution of X₁+X₂ if both of the variables are independent? Show this by using MGF's. Find P(X₁+X227).
= Suppose that independent Bernoulli trials, each having probability p 0.4, of being a success are performed until a total of r = 3 success is achieved. Let X be the number of trials required. a) What are the possible values for X? b) IfX = n, find P (X = n). c) What is the probability of having 3 success before having 5 failures?
4. Let X1, X2, ., Xn,... be a sequence of i.i.d. random variables with Poisson(A = 8) distribution. Prove that for some n, P(X1 + X2 +.+ Xn > 9n) < 0.001
A.2) The time between successive customers coming to the market is assumed to have Exponential distribution with parameter lambda. a) If X1, X2. ..., Xp are the times, in minutes, between Successive customers selected randomly, estimate the parameter of the distribution. b) The randomly selected 15 times between successive customers are found as 1.8, 1.2, 0.8, 1.4, 1.2, 0.9, 0.6, 1.2, 1.2, 0.8, 1.5, 1.8, 0.9, 1.5 and 0.6 mins. Estimate the mean time between successive customers, and write down the distribution function. c) In order to estimate the distribution parameter with 0.4 error and 4% risk, find the minimum sample size.

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS