What is the value of the constant c for p(x) to qualify as a probability mass function? ?(?)=?(1/4)x-1 ?? ? = 1, 2, 3, 4, 5, ... and p(x) = 0 otherwise. How would you get c{1-1/4}-1 = 1
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What is the value of the constant c for p(x) to qualify as a probability mass
?(?)=?(1/4)x-1 ?? ? = 1, 2, 3, 4, 5, ...
and p(x) = 0 otherwise.
How would you get c{1-1/4}-1 = 1
Step by step
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- 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)It has something to do with statistics and probabilityThe 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 0In each case, determine the value of the constant c that makes the probability statement correct. (Round your answers to two decimal places.) (a) Φ(c) = 0.9850 (b) P(0 ≤ Z ≤ c) = 0.2995 (c) P(c ≤ Z) = 0.1314 (d) P(−c ≤ Z ≤ c) = 0.6528 (e) P(c ≤ |Z|) = 0.0128 You may need to use the appropriate table in the Appendix of Tables to answer this question.Q.3 The probability density function for a continuous random variable X is fx(x) = {a + bx²; 0A individual, with a utility function lnW and an initial wealth level W0, is faced with a fair gamble of winning or losing $h (where W0 > h > 0) with 50-50 chance. (a) Is this individual risk averse? Explain.(b) Suppose that the individual is willing to pay up to an amount of f in order to avoid such a gamble. Give the equation that determines f, and solve the equation for f (i.e., express f in terms of W0 and h). (c) Show that f increases as h increases.Event A is my wife cooking dinner tonight. It has been determined that P(A) = 0.15. What is P(not A)?Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON