Recent content by SandMan249

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    MLE of P(X<2) - Exponential distribution

    Homework Statement Find the MLE of θ = P (X≤ 2) in a random sample of size n selected from an exponential distribution EXP(λ) Homework Equations f(x, λ) = λ e^(-λx) F(x, λ) = 1 - e^(-λx) The Attempt at a Solution I know how to find the MLE of the mean of an exponential...
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    How Does the Constraint θ ≤ 1/4 Affect the MLE in Bernoulli Trials?

    Thank you. In this case, since the function is simply: θ(hat) = 1/2 (a constant) The maximum will lie at 1/4 Correct?
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    How Does the Constraint θ ≤ 1/4 Affect the MLE in Bernoulli Trials?

    Homework Statement Two independent bernoulli trials resulted in one failure and one success. What is the MLE of the probability of success θ is it is know that θ is at most 1/4 Homework Equations f(x,θ) = θx (1-θ)1-x The Attempt at a Solution Now, I know how to find the likelihood...