Verify that the following function is a probability mass function, and determine the requested probabilities. [Give exact answers inform of fraction.]f(x) = (3/4)(1/4)*, x = 0,1,2,...(a) P(X = 2) =(b) P(X ≤ 2) =(c) P(X > 2) =(d) P(X ≥ 1) =

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Answered: Verify that the following function is a…

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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Suppose that a decision maker's risk atitude toward monetary gains or losses x given by the utility function(x) = (50,000+x) 34/2. Suppose that a decision maker has the choice of buying a lottery ticket for $5, or not. Suppose that the lottery winning is $1,000,000, and the chance of winning is one in a thousand. Then..... O The decision maker should not buy the ticket, as the utility from not buying is 223.6, and the expected utility from buying is 223.59. The decision maker should not buy the ticket, as the utility from not buying is 223.6067, and the expected utility from buyingis 223.6065. O The decision maker should buy the ticket, as the utility from not buying 223.60, and the utility from buying is 224.4. The decision maker should buy the ticket, as the utility from not buying 223.6065, and the utility from buying is 223.6067.
Which of the following is a valid cumulative distribution function? Note: the arrow means the line extends to +inf.
Q3. Exponential Distribution has a memoryless property. Intuitively, it means that the probability of customer service answering you call (assuming waiting time is exponential) in the next 10 mins is the same, no matter if you have waited an hour on the line or just picked up the phone. Formally, if X ∼ exponential(λ), f(x) = λ exp(- λx), and t and s are two positive numbers, use the definition of conditional probability to show that P(X > t + s | X > t) = P(X > s).Hint: Find the cdf of X first, and note that P(X > t + s Ç X > t) = P(X > t + s)
The pdf of the time to failure of an electronic component in a copier (in hours) is f (x) = [exp (-x/3100)]/3100 for x > 0 and f (x) = 0 for x ≤ 0. Determine the probability that:(a) A component lasts more than 1180 hours before failure.(b) A component fails in the interval from 1180 to 2010 hours.(c) A component fails before 3010 hours.(d) Determine the number of hours at which 11% of all components have failed.(e) Determine the mean.Round your answers to three decimal places (e.g. 98.765).
The time t (in hours) required for a new employee to succesfully learn to operate a machine in a manufacturing process is described by the probability function f(t) = kt/16 – t for 0
The probability function of the amount of soft drink in a can is f(x)=4cx for11.5 <X< 12.5 oz. Determine the value of c such that f(x) represents a p.d.f..Then, find the following probabilities:(a) P(X > 11.5), (b) P(X < 12.25), and (c) P(11.75 <X< 12.25).

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Verify that the following function is a probability mass function, and determine the requested probabilities. [Give exact answers in form of fraction.] f(x) = (3/4)(1/4)*, x = 0,1,2,... (a) P(X= 2) = (b) P(X ≤ 2) = (c) P(X > 2) = (d) P(X ≥ 1) =