Let X1, X2 be a random sample of size 2 from Bernoulli distribution with pmf as f(x, theta) = begincases theta^x(1-theta)^1-x, & x = 0, 1 0, & otherwise endcases. Then X1+X2 is sufficient for theta if P[X1 = x1, X2 = x2 mid (X1+X2) = t] is equal to:

Q33Section I (Objective (Q1–Q80))33 of 80

Statistical Inference — conditional distribution given the total

Let $X_1$ , $X_2$ be a random sample of size 2 from Bernoulli distribution with pmf as $f(x, \theta) = \begin{cases} \theta^x(1-\theta)^{1-x}, & x = 0, 1 \ 0, & \text{otherwise} \end{cases}$ . Then $X_1+X_2$ is sufficient for $\theta$ if $\mathbb{P}[X_1 = x_1, X_2 = x_2 \mid (X_1+X_2) = t]$ is equal to:

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