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  1. Con-Tester

    Reference for 1-exp(-t/T)

    After much scouring through books and journals, the closest thing I was able to find is on this page—look for the heading “6.3 Poisson process” where it says: My suggestion would be to write it as “1 – exp(–t/T)” in the body of the paper, and add a footnote with a reference to the above...
  2. Con-Tester

    Probability, when i know the mean and std. dev

    The answer to the first question you gave is correct: P(x < 500.000) = 0,38%. To answer the second one, ask yourself two questions: (1) What is the standard z-score for P = 5%? (2) Given the mean, a sample value, and a standard z-score, how does one calculate the standard deviation? You can...
  3. Con-Tester

    sas function that works with date variables

    Yes, it will work correctly for all valid dates, including leap years, because, as mentioned previously, SAS stores dates as the integer number of days since 01 January 1960, where a negative value is a date prior to that reference date. (However, note that there are upper and lower limits to...
  4. Con-Tester

    sas function that works with date variables

    It must be clearly understood that SAS has just two data types, namely text and numeric. The numeric data type is in all cases the IEEE 754 double-precision floating-point type (8-byte real). SAS doesn’t even distinguish between integer and floating-point numeric types; all numeric types are...
  5. Con-Tester

    Compound Probabilities

    To expand on Karabiner’s answer, there are four possible damage scenarios to consider, namely: Break AND Burn; Break AND (NOT Burn); (NOT Break) AND Burn; and (NOT Break) AND (NOT Burn). Each scenario has a probability of occurring associated with it that is straightforward to evaluate, and...
  6. Con-Tester

    Simultaneous convoluted linear equations

    Both equations reduce to y = x, so there's no unique solution.
  7. Con-Tester

    Dependant Probability - Theoretical and Experimental have different outcomes?

    I think your calculation is incorrect. It doesn't seem to exhaust all possible 3-coin selection paths, for example 0.6 --> 0.5 --> 0.9. A probability tree may prove helpful. Assuming the coins are otherwise indistinguishable apart from their bias, there are 43 distinct ways to select a 3-coin...
  8. Con-Tester

    Selecting the first record for a particular variable based on a condition

    Try following your sort procedure with a second one, thus: proc sort data=master_b nodupkey; by acctnum; run; Note that your sort procedure will pick out the latest occurrence (assuming "month" is numeric) rather than the earliest.
  9. Con-Tester

    Simple Probability

    Enumerate all 36 possible outcomes, count the qualifying hits and you should soon see where your thinking goes wrong.
  10. Con-Tester

    Probability Question

    The values you assign to P(B | A) for the different exam situations are all incorrect, suggesting that you don't properly understand the problem.
  11. Con-Tester

    Probability Question

    Your answer appears to be incorrect, assuming that it is equiprobable that one is faced with one of an easy, normal, or difficult exam. Conditional probability: P(A & B) = P(B) × P(B | A) Let A = "Answers first question correctly" and B = "Answers second question correctly." On the aforesaid...
  12. Con-Tester

    Have no idea how to go about this issue

    You can turn the problem around by asking what the probability is that none of the five people submits false information. If the probability is p = 0.15 that a given applicant submits false information, then the probability that s/he won’t is p’ = 1 – p = 1 – 0.15 = 0.85. For five independent...
  13. Con-Tester

    Please help with the following question

    Yes, σ = 0.51 is correct. You can verify this by using the aforesaid online normal distribution calculator. In fact, I would recommend that you do so.
  14. Con-Tester

    Please help with the following question

    First, read here on the basics of how to combine normally distributed random variables. Next, figure out how to apply such a combination to the problem at hand. (Hint: The mean length μ is the same for each link, as is the standard deviation σ.) Finally, you can use this normal distribution...
  15. Con-Tester

    Finding Standard Deviation in a binomial distribution : Help Please

    Read here. Note that you can determine P, the probability of a success on any single throw, from the information given. In fact, more information was given than is strictly necessary: You know that it's a binomial distribution (a throw either succeeds or fails), and that n = 2 (two throws)...
  16. Con-Tester

    Probability and quality control

    That’s the nub of the problem. There is no obvious way to relate the process time to the failure rate. Indeed, the two may be entirely unrelated. For example, the failures could be the result of inherent flaws and/or weaknesses in the raw input materials, and no amount of slowing down the...
  17. Con-Tester

    I made up a counting/probability problem and I'm having trouble thinking about it the right way

    … to which I would add that reflecting on the so-called “Birthday Paradox” will certainly provide much illumination.
  18. Con-Tester

    Dice Rolls and the Environment

    Your take on the situation is entirely correct: A fair die that strikes another object or falls off the table does not suddenly become biased. The fact is that hitting a book or falling off the table does not make the outcome of a given toss any more (or less) predictable, and is therefore...
  19. Con-Tester

    Who is most likely to win, and exactly how likely?

    No problem. But note that I’ve made a notational error. The accepted way of writing the normal distribution is “x ~ N(μ, σ²)”—i.e., the second argument is the variance σ², not the standard deviation σ, as I had it. So, in the second paragraph it should read: s₁ ~ N(55, 10²) s₂ ~ N(50, 20²) d...
  20. Con-Tester

    Who is most likely to win, and exactly how likely?

    Refer to In your example, let the player with the higher mean score be s₁ ~ N(55, 10) and the one with the lower mean score be s₂ ~ N(50, 20). Then d = (s₁ – s₂) ~ N(55 – 50, √(10²+20²)) ≡ N(5, √500). Note that the...