Let X, X, ..., XN be independent, uniformly distributed on the continuous domain [0,0] for some...

  

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Let X₁, X₂, ..., XN be independent, uniformly distributed on the continuous domain [0,0] for some 8. What is the Maximum likelihood estimate for 0? Your Solution: Q5.2 Binomial distribution I (5pt) Suppose we observe the values of M iid random variables Y₁, Y₂,...,YM drawn from a single Binomial distribution B(n, 0). A Binomial distribution models the number of 1's from a sequence of n independent Bernoulli variables with parameter 0. In other words, P(Y₁ = k) = (n.) 0² (1 - 0)ª- -k -k n! k! (n − k)! Write a formula for the negative log likelihood function IM (0). Your function should depend on the random variables Y₁, Y2, ..., YM and 0. Your Solution: = -0 (1-0)n- Q5.3 Binomial distribution II (5pt) Consider two independent Binomial random variables Y₁ and Y₂ with the same parameters n = 5 and 0. The sampled values for Y₁ and Yvate Wind are (0, 0, 1, 1, 1) and (0, 1, 0, 1, 1). Therefore, Y₁ = 3 and Y₂ = 3. Compute the maximum likelihood estimate for the 2 samples. Show yourettings to a work. Let X₁, X₂, ..., XN be independent, uniformly distributed on the continuous domain [0,0] for some 8. What is the Maximum likelihood estimate for 0? Your Solution: Q5.2 Binomial distribution I (5pt) Suppose we observe the values of M iid random variables Y₁, Y₂,...,YM drawn from a single Binomial distribution B(n, 0). A Binomial distribution models the number of 1's from a sequence of n independent Bernoulli variables with parameter 0. In other words, P(Y₁ = k) = (n.) 0² (1 - 0)ª- -k -k n! k! (n − k)! Write a formula for the negative log likelihood function IM (0). Your function should depend on the random variables Y₁, Y2, ..., YM and 0. Your Solution: = -0 (1-0)n- Q5.3 Binomial distribution II (5pt) Consider two independent Binomial random variables Y₁ and Y₂ with the same parameters n = 5 and 0. The sampled values for Y₁ and Yvate Wind are (0, 0, 1, 1, 1) and (0, 1, 0, 1, 1). Therefore, Y₁ = 3 and Y₂ = 3. Compute the maximum likelihood estimate for the 2 samples. Show yourettings to a work.

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