Recent content by Amannequin

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    Any idea on how to integrate the following?

    Homework Statement The c.d.f. of a random variable X is given by the following formula F(x) = 1 - e-x2 x≥0 Find M(t). Moment generating function. The Attempt at a Solution I've found the pdf as f(x) = F'(x) = 2xe-x2 x≥0 To determine M(t) I need to do the following...
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    Poisson Probability: At Least 50% Defective Brake Lights

    Homework Statement Suppose that 1% of cars have defective brake lights and n cars are to be inspected. How large should n be for the sample to have a probability of at least 50% of containing a car with a defective brake light? Give an answer using a Poisson approximation with an appropriate...
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    Proving Prime p≥3 Satisfies pr ≡ 1, 5, 7 or 11 (mod 12)

    Homework Statement If p is a prime and p>3, show that pr\equiv1,5,7 or 11 (mod12) Homework Equations The Attempt at a Solution Do I go about this by knowing that any prime p greater than 3 is of the form 6n+1 or 6n+5? Any direction on how to go about this will be helpful. Thanks.
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    Rolling a Fair Die: Probability of Getting At Least One Six After Multiple Rolls

    Homework Statement How many times do we need to roll a fair die to get a better than evens chance of at least one six? The attempt at a solution Let n be the number of rolls. Am I trying to find how large n must be so P(At least one six)≥ 1/2? I'm working on the basis that I need to solve...
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