3. Check whether the following can be looked upon as probabilityfunctions (defined in each case only for the given values of x) andexplain your answers:(a) f(x)=1/4(b) f(x) = (x+1)/10(c) f(x) = (x-2)/5(d) f(x)=x²/30for x=0, 1, 2, 3, orfor x = 0, 1, 2, or 3;for x = 1, 2, 3, 4, or 5;for x = 0, 1, 2, 3, or 4.

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Answered: 3. Check whether the following can be…

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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P(A)=0.15,P(A')=0.85,P(B|)=0.3,ANDP(B|A'=0.7 The possibility of event a given that event B has occurred is rounded to the nearest tenth as needed
(Sec. 3.2) A student is required to enroll in one, two, three, four, five, six on the desired courseload) at a local university. Let Y the number of classes the next student enrolls themselves in. The probability that y classes are selected is known to be proportional to y+1, in other words the pmf of Y is given by p(y) = k(y+1) for y 1,...,7, and 0 otherwise (a) What is the value of k? or seven classes (depending (b) What is the probability that at most four classes are enrolled in? (c) What is the probability that a student enrolls in between three and five classes (inclusive)? y? /40 for y 1,.,7 be the pmf of Y? Explain why why not (d) Could p(y) or
For each of the following, determine whether the given values can serve as the values of a probability dis-tribution of a random variable with the range x = 1, 2, 3, and 4:(a) f(1) = 0.25,f(2) = 0.75,f(3) = 0.25, and f(4) =−0.25;(b) f(1) = 0.15,f(2) = 0.27,f(3) = 0.29, and f(4) = 0.29;(c) f(1) = 119 , f(2) = 1019 , f(3) = 219 , and f(4) = 519 .
1. Answer the following questions using the probability tree below: .2 .3 X .3 .8 a Y (a) What is the value of z? (b) What is the probability of X occurring? (c) What is Pr[Xa] (Note: Pr[Xa] = Pr[X and a].) (d) What is Pr[X_or a]? (e) What is Pr[a|X]? (f) What is Pr[c]?
Q.#3 (a) In a certain industrial facility, accidents occur infrequently. It is known that the probability of an accident on any given day is 0.005 and accidents are independent of each other.(i) What is the probability that in any given period of 400 days there will be an accident on one day?(ii) What is the probability that there are at most three days with an accident?(iii) Find ?(2 < ? ≤ 4 /? < 3)
A decision maker has a utility function for monetarygains x given by u(x) (x 10,000)1/2. a Show that the person is indifferent between the sta-tus quo and L: With probability 13, he or she gains $80,000 L: With probability 23, he or she loses $10,000b If there is a 10% chance that a painting valued at$10,000 will be stolen during the next year, what is themost (per year) that the decision maker would be willingto pay for insurance covering the loss of the painting?

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3. Check whether the following can be looked upon as probability functions (defined in each case only for the given values of x) and explain your answers: (a) f(x)=1/4 (b) f(x) = (x+1)/10 (c) f(x)=(x-2)/5 for x=0, 1, 2, 3, or for x = 0, 1, 2, or 3; for x = 1, 2, 3, 4, or 5: