Let A be an event and Let S be the Sample Space. Prove that the probability function, P(A) = n(A) / n(S), satisfies the three axioms below. 1) P(Ai) > 0 2) P(S) = 1 3) P(U Ai) = (Summation of all values 'i') P(Ai)

Let A be an event and Let S be the Sample Space. Prove that the probability function, P(A) = n(A) / n(S), satisfies the three axioms below. 1) P(Ai) > 0 2) P(S) = 1 3) P(U Ai) = (Summation of all values 'i') P(Ai)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

find the expected value of the probability experiment with outcomes X1, X2,... x1=2, x2=6, x3=4, x4=8, P(x1)=1/5, P(x2)=2/5, P(x3)= 1/5, P(x4)=1/5 the expected value of the probability experiment is E=
12
11 the probability distribution of discete random variable x is given by p (X=x) = k÷ x+1 for x = 1,2,3 a) find the value of K where K is constant b) compute P(x=2) C) compute p(x=2 or x=3)
There are two boxes. In each box there are 4 cards with a different number printed on it. The four cards have been numbered as 1,2,3,4 in each box. Two cards are drawn random from each box. The random variable X represents the difference between the number on the card from box 1 minus the number on the card from box 2.a) Find the mean of this probability distribution. (i.e. Find E[X] )b) Find the variance and standard deviation of this probability distribution.(i.e. Find V[X] and SD[X])The random variables M and W are defined as follows:M = X+5 and W = (1/2)X+5c) Find E[M] and E[W].d) Find V[M] and V[W].e) Mary and William play a game using the cards in the above boxes. Randomly two cards are drawn, and Mary records his score using the random variable M and William uses the random variable W. They repeat this for a large number of times and compare their scores. Comment on any likely differences or similarities of their scores.
An urn contains 4 red, 4 blue, 4 green marbles Three marbles are drawn with replacement (put marble back in before drawing the next one). Let X be the random variable representing the number of green marbles drawn . Compute the probabilities : ( a) Pr X=0) (b) Pr X=1) (c) Pr * (X = 3)
Random variable X has the binomial distribution with n=100 and p=0.25. By using binomial probability table, find a)p(x<20) b)p(x<=15) c)p(20<x<30)
In a factory, there were 18 accidents involving machinery in the last six months. (a) State the probability distribution (with its parameter and parameter value) thatcan describe the number of accidents in the factory in any single month (b) Calculate the probability that there will be 5 accidents in the factory next month (c) Calculate the probability that there will be less than 4 accidents in the factoryduring the next months. (d) Calculate the probability that there will be more than 2 accidents in the factoryduring the next months.
Find the expected value of probability function Fonksiyonun beklenen değerini bulunuz 6 - 1 2 4 P(X) 0,25 0,15 0,10 0,25 0,25 О a) 1.3 O B) 1.1 O NS) 1,2 O D) 3 Ο ΤΟ) 2.1 3.
According to a study by Weight Loss R US of their live-in weight loss program, the people who follow his program lose between 6 and 14 pounds a month until they approach trim body weight. Let's suppose that the weight loss is uniformly distributed. We are interested in the weight loss of a randomly selected individual following the program for one month. Suppose it is known that the individual lost more than ten pounds in a month. Find the probability that he lost less than 10 pounds in the month. (round your answers to 4 decimals.)
there is small parking lot behind a Floral Shop that has two parking lot spaces. Let X be the number of cars parked in the parking lot at midday. The probability distribution of X is given by P(X=x)= 4-x x=0 1 2 9 (i) Construct the probability distribution table (ii) What is the probability that there will be at most 1 car in the parking lot? (iii) Calculate the expected number of cars in the parking lot at midday
A quality inspector picks a sample of 15 items at random from a manufacturing process known to produce 10% defective items. Let X be the number of defective items found in the random sample of 15 items. Assume that the condition of each item is independent of that of each of the other items in the sample. The probability distribution of X is provided in the excel file. Use simulation to generate 500 values of this random variable X. A) Use simulation to generate 500 values of this random variable X.B) Calculate the mean and standard deviation of the simulated values. How do they compare to the mean and standard deviation of the given probability distribution? Use excel to help please and attach... Previous writer did not include part A in excel Note: These probabilities were generated by a binomial distribution,. For now, you can just take these probabilities as given. Number of defective items in a random sample of 15 items # of defectives Probability 0…
A delivery truck travels from point A to point B and back using the same route each day. There are four traffic lights on the route. Let X1 denote the number of red lights the truck encounters going from A to B and X2 denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (X1, X2) is given by