6. Suppose that X₁ and X₂ are IID discrete random variables from either-12-21₁or,p(x;0= 1);x = 1,2,313'When we observe X₁ = 1 and X2 = 2, find the mle of 0.p(x; 0 = 2)x = 1,2,3

To find the maximum likelihood estimator (MLE) of θ (theta) given the observations X₁ = 1 and X₂ =…

Answered: 6. Suppose that X₁ and X₂ are IID…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E

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1. Show that if X' , Y' are the deviations of the random variables X and Y from their respective means, then 2 i)r = 1-E (- ii) r = -1 ++E 2N 2N lox Deduce that -1srs1.
8. Two independent random variables X1=(-1.0.1) and X2-(0.1) can take the following probability values: P(X1=-1)=p, P(X1=0)=p/2, P(X 1=1) 1-3p/2, P(X_2=0)=p, PIX 2=1)=1-D. If Y-X1 X2, determine the average E(Y). E(Y) =? X₁ = (-1,0, 1) y X₂ = (0, 1) P(X₁ = -1) = p P(X₁ = 0) = { P(X₁ = 1) = 1 - T P(X₂ = 0) = p P(X₂= 1) = 1-p Y = X₁ + X₂
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An ordinary (fair) coin is tossed 3 times. Outcomes are thus triple of “heads” (h) and tails (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of tails in each outcome. For example, if the outcome is hht, then R (hht)=1. Suppose that the random variable X is defined in terms of R as follows X=6R-2R^2-1. The values of X are given in the table below. A) Calculate the values of the probability distribution function of X, i.e. the function Px. First, fill in the first row with the values X. Then fill in the appropriate probability in the second row.
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6. Suppose that X₁ and X₂ are IID discrete random variables from either 12-12-21 1 or, p(x;0= 1) = 1 3' When we observe X₁ = 1 and X₂ = 2, find the mle of 8. p(x; 0 =2) x = 1,2,3 = r = 1,2,3