Question

2. Let us consider a box containing 5 balls, where each ball is either white or blue, but we have no information about the ball or box. You are allowed to choose 4 balls at random from the bag with replacement. Let the pmf of X1, X2, X3, and X4, be the Bernoulli(\theta/5) \begin{equation} X_i = \begin{cases} 1 & \text{if ith ball choosen is blue} \\ 0 & \text{else} \end{cases} \end{equation} After doing the experiment, the following values for Xi's are observed, x1 = 0, x2 = 0, x3 = 1, x4 = 0. i. For each possible value of \(\theta\), find the probability of the observed sample, (x1,x2,x3,x3) = (0,0,1,0) ii. For which value of \(\theta\) is the probability of the observed sample the largest?

          2. Let us consider a box containing 5 balls, where each ball is either white or blue, but we
have no information about the ball or box. You are allowed to choose 4 balls at random
from the bag with replacement. Let the pmf of X1, X2, X3, and X4, be the Bernoulli(\theta/5)
\begin{equation*}
X_i = \begin{cases}
1 & \text{if ith ball choosen is blue} \\
0 & \text{else}
\end{cases}
\end{equation*}
After doing the experiment, the following values for Xi's are observed,
x1 = 0, x2 = 0, x3 = 1, x4 = 0.
i. For each possible value of \(\theta\), find the probability of the observed sample,
(x1,x2,x3,x3) = (0,0,1,0)
ii. For which value of \(\theta\) is the probability of the observed sample the largest?

2. Let us consider a box containing 5 balls, where each ball is either white or blue, but we
have no information about the ball or box. You are allowed to choose 4 balls at random
from the bag with replacement. Let the pmf of X1, X2, X3, and X4, be the Bernoulli(θ/5)

Xi =
1 if ith ball choosen is blue

0 else

After doing the experiment, the following values for Xi's are observed,
x1 = 0, x2 = 0, x3 = 1, x4 = 0.
i. For each possible value of θ, find the probability of the observed sample,
(x1,x2,x3,x3) = (0,0,1,0)
ii. For which value of θ is the probability of the observed sample the largest?

Added by Dawn B.

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