7An experiment can be a success with the probability p anda failure with the probability 1 - p.The conditional probability P(m) for achieving the desired result after msuccessful trials is11P(m) = 1(w > 1).Find the expectation of the number of independent trials necessary forachieving the desired result.m3

Let Pn(A) denotes the probability of n trials.Pn,m is exactly m success in ntrials.…

Answered: An experiment can be a success with the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A particle executes an unrestricted simple random walk on the line with p=0.7 and q=0.3. Its position at time n is represented by the random variable Xn, n = 0, 1,...; Xo = 0. (a) Calculate the values of the following probabilities. (i) P(X5 = -2) (ii) P(X6 = 2) (b) Calculate the probability that the particle returns to its starting point for the first time after 8 steps. (c) After the particle has been moving for some time, it is observed to be located at the point +3. (i) Calculate the probability that the particle will ever return to the origin from the point +3. (ii) Calculate the probability that starting from the point +3, the particle will visit the point +8 without first visiting the origin.
4) If there is a 25% chance of a spinner landing on blue. In 20 trials a) What is the expected value? [K/1] b) What is the probability of that number of success occurring? (Solve the probability of a) [T/2] c) Does your answer in b) make sense? Explain how the probability and expected values relate. [T/1, C/1]
In game of roulette, a player can bet on the 1/38 probabilty of metal batt landa on 1the player gets to keep the paid to play the game and the player is awarded an additional 140 Otherwise, the player is awarded nothing and the casino takes the player's $4. Find the expected value E(x) to the player for one play of the game to player in a game of chance, then E(x) is negative. This value gives the average amount the player can expect to lose.
The annual rainfall (in inches) in a certain region is normally distributed with µ = 40 and σ = 4. What is the probability that starting with this year, it will take more than 10 years before a year occurs having a rainfall of more than 50 inches? Suppose the rainfall in each year is independent of the rainfall in other years and the distribution of rainfall in each year is the same as in the present year.
3
For the M/M/N/o system, the probability that an arrival will find all servers busy and will be forced to wait in queue is an important measure of performance of the M/M/N/∞ system. This probability is given by PQ N!(1 – p/N) | and is known as the Erlang C formula. Please derive the equation. What is the expected number of customers waiting in the queue (not in service)?
The time that it takes to service a car is an exponential random variable with rate 1.1. If A brings his car in at time 0 and B brings his car in at time t, what is the probability thatB’s car is ready before A’s? Assume that the service times are independent, and the servicebegins upon arrival.2. If both cars are brought in at time 0, with work starting on B’s car only when A’s car has beencompletely serviced, what is the probability that B’s car is ready before 2? Detailed explanation and calculation would be much appreciated.
The complement of an event is all possible outcomes not in the event. For example: If A = at least 3 girls are born to a family with 6 kids. Then A' = A compliment is what happens if there are not at least 3 girls = less than 3 girls born to the family. A useful formula: P(A) + P(A' ) = 1 or P(A') = 1 - P(A). If P(A) = 0.194, what is P(A')?
8. The time (in minutes) that it takes a car mechanic to replace a car battery is a random variable X that follows an exponential distribution with mean 15 minutes. a) Find P(14 < X < 22). Round off your answer to two decimal places. x 22 1 P(14 < X <22) = √₂/1² 15 e 15dx = P(x < 22) — P(x < 14) x 15 122 = e 15 22 1 - e 14 or 0.8 = = 22 14 = −e 15 + e15 = 0.16254≈ 0.16 - (1 – b) Find the 80th percentile. Round off to the nearest whole number. 1 X S 15 14 e 15 t e 15 dt X 0.8 = 1 e 15 X e 15 = = 0.2 14 22 = e 15 e 15 = 0.16 x — = ln (0.2). This gives x = 24.14156 15
Event A is my wife cooking dinner tonight. It has been determined that P(A) = 0.15. What is P(not A)?
4) What number of drones N makes your second-morning observations as likely as possible?5) Assuming again that the probability that N = n is proportional to the probability of observing this specificdata on the second day, find again the smallest nmax so that P (N ≤ nmax) = 0.95.
Suppose Xt denotes the unknown whose value is the success count for ?ttrials of a Bernoulli Process with success rate p and Wn the unknown whose value is the number of trials to have the nth success. Then, the probability that the number of trials to get the 7th success is at most 10 is which of the following? (A) P(X10≥7)P(X10≥7) (B) P(X7<10)P(X7<10) (C) P(X10<7)P(X10<7) (D) P(W7≥10)

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