Mike has a deck of standard poker cards with some cards missing. He wants to estimate the probability, p, of drawing a spade. Every day he makes an experiment. At the end of each experiment, he records the maximum likelihood estimator of the probability of observing a spade and places the drawn card back and shuffles the deck. Let X; be a random variable, taking value 1 if the i-th card draw of an experiment results in an even number and 0 if it results in an odd number. Clearly, X, ~ Bernoulli(p). Recall the MLE of a Bernoulli is p MLE The following are the outcomes of 5 experiments, one of which involved 8 card draws, two of which involved 6 card draws and two of which involved 4 card draws. Which experiments lead to the same MLE of p? Select all that apply. O (1 = 0, x2 = 1, r3 = 0, x4 = 0, r; 1, 6 = 0, x7 = 1, Is = 1, xg = 0, r10 = 1, 111 = 0, 112 = 0) O (1 = 1, a2 = 0, r3 = 1, x4 = 1) O ( = 0, x2 = 0, r3 = 0, r4 = 0) O (21 = 0, x2 = 1, £3 = 0, T4 = 0, x5 = 0, x6 = 0, r7 = 1, rg 0) O (1 = 0, x2 = 1, r3 = 0, a4 = 1, x; = 0, x6 = 0, x7 = 0, 1s = 1, ¤9 = 0, r10 = 0, u = 0, x12 =0) O (#1 = 1, x2 = 1, £3 = 0, x4 = 0, r5 = 1, x6 = 0, x7 = 0, rs = 1)
Mike has a deck of standard poker cards with some cards missing. He wants to estimate the probability, p, of drawing a spade. Every day he makes an experiment. At the end of each experiment, he records the maximum likelihood estimator of the probability of observing a spade and places the drawn card back and shuffles the deck. Let X; be a random variable, taking value 1 if the i-th card draw of an experiment results in an even number and 0 if it results in an odd number. Clearly, X, ~ Bernoulli(p). Recall the MLE of a Bernoulli is p MLE The following are the outcomes of 5 experiments, one of which involved 8 card draws, two of which involved 6 card draws and two of which involved 4 card draws. Which experiments lead to the same MLE of p? Select all that apply. O (1 = 0, x2 = 1, r3 = 0, x4 = 0, r; 1, 6 = 0, x7 = 1, Is = 1, xg = 0, r10 = 1, 111 = 0, 112 = 0) O (1 = 1, a2 = 0, r3 = 1, x4 = 1) O ( = 0, x2 = 0, r3 = 0, r4 = 0) O (21 = 0, x2 = 1, £3 = 0, T4 = 0, x5 = 0, x6 = 0, r7 = 1, rg 0) O (1 = 0, x2 = 1, r3 = 0, a4 = 1, x; = 0, x6 = 0, x7 = 0, 1s = 1, ¤9 = 0, r10 = 0, u = 0, x12 =0) O (#1 = 1, x2 = 1, £3 = 0, x4 = 0, r5 = 1, x6 = 0, x7 = 0, rs = 1)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Mike has a deck of standard poker cards with some cards missing. He wants to estimate the
probability, p, of drawing a spade. Every day he makes an experiment. At the end of each
experiment, he records the maximum likelihood estimator of the probability of observing a spade
and places the drawn card back and shuffles the deck. Let X; be a random variable, taking value 1 if
the i-th card draw of an experiment results in an even number and 0 if it results in an odd number.
Clearly, X, ~ Bernoulli(p). Recall the MLE of a Bernoulli is p MLE
The following are the outcomes of 5 experiments, one of which involved 8 card draws, two of which
involved 6 card draws and two of which involved 4 card draws. Which experiments lead to the same
MLE of p? Select all that apply.
O (1 = 0, x2 = 1, r3 = 0, x4 = 0, r; 1, 6 = 0, x7 = 1, Is = 1, xg = 0, r10 = 1, 111 = 0, 112 = 0)
O (1 = 1, a2 = 0, r3 = 1, x4 = 1)
O ( = 0, x2 = 0, r3 = 0, r4 = 0)
O (21 = 0, x2 = 1, £3 = 0, T4 = 0, x5 = 0, x6 = 0, r7 = 1, rg 0)
O (1 = 0, x2 = 1, r3 = 0, a4 = 1, x; = 0, x6 = 0, x7 = 0, 1s = 1, ¤9 = 0, r10 = 0, u = 0, x12 =0)
O (#1 = 1, x2 = 1, £3 = 0, x4 = 0, r5 = 1, x6 = 0, x7 = 0, rs = 1)
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