Your statistics professor hands you a fair die, with each side having the same chance of being the uppermost face. You are asked to toss the die 7 times and count the number of times the die shows a topside of six. This count is represented by the random variable X. (a) Complete the probability distribution of X below. Use four decimals in each of your entries. X P(X=x) 0 1 2 3 4 5 6 (b) From the distribution you found in part (a), what can you say about the distribution of X? The distribution of X is ? 7 0.00000357 (Enter your answers to two decimals.) ✓, with an mean of sixes and a standard deviation of Sixes. (c) As requested, you have tossed the die 7-times and observed X = 5 sixes. If you were to repeat the 7-tosses of this die, what is the probability you will observe at least the same number of sixes as this? Enter your answer to four decimal places. (d) In part a) you just gave the distribution for how many times a 'fair' die tossed 7 times should show a six. Let's say you tried this experiment, and you happened to observe 6 out of the 7 times rolling a 6 (aka P(X= 6)). Feeling suspicious you try another 7 times...and again got either 6 or all 7 (out of 7) to be a six(aka P(X ≥ 6)). Compare with what should likely have happened (refer to part a). What would you say this information means? Select the most appropriate answer.
Your statistics professor hands you a fair die, with each side having the same chance of being the uppermost face. You are asked to toss the die 7 times and count the number of times the die shows a topside of six. This count is represented by the random variable X. (a) Complete the probability distribution of X below. Use four decimals in each of your entries. X P(X=x) 0 1 2 3 4 5 6 (b) From the distribution you found in part (a), what can you say about the distribution of X? The distribution of X is ? 7 0.00000357 (Enter your answers to two decimals.) ✓, with an mean of sixes and a standard deviation of Sixes. (c) As requested, you have tossed the die 7-times and observed X = 5 sixes. If you were to repeat the 7-tosses of this die, what is the probability you will observe at least the same number of sixes as this? Enter your answer to four decimal places. (d) In part a) you just gave the distribution for how many times a 'fair' die tossed 7 times should show a six. Let's say you tried this experiment, and you happened to observe 6 out of the 7 times rolling a 6 (aka P(X= 6)). Feeling suspicious you try another 7 times...and again got either 6 or all 7 (out of 7) to be a six(aka P(X ≥ 6)). Compare with what should likely have happened (refer to part a). What would you say this information means? Select the most appropriate answer.
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:Your statistics professor hands you a fair die, with each side having the same chance of being the uppermost face. You are asked to toss the
die 7 times and count the number of times the die shows a topside of six.
This count is represented by the random variable X.
(a) Complete the probability distribution of X below. Use four decimals in each of your entries.
P(X= z)
1
2
3 4 5 6
(b) From the distribution you found in part (a), what can you say about the distribution of X?
The distribution of X is ?
7
0.00000357
(Enter your answers to two decimals.)
♥, with an mean of
sixes and a standard deviation of
(c) As requested, you have tossed the die 7-times and observed X = 5 sixes. If you were to repeat the 7-tosses of this die, what is the
probability you will observe at least the same number of sixes as this? Enter your answer to four decimal places.
(d) In part a) you just gave the distribution for how many times a 'fair' die tossed 7 times should show a six. Let's say you tried this
experiment, and you happened to observe 6 out of the 7 times rolling a 6 (aka P(X= 6)). Feeling suspicious you try another 7 times...and
again got either 6 or all 7 (out of 7) to be a six(aka P(X ≥ 6)). Compare with what should likely have happened (refer to part a). What would
you say this information means? Select the most appropriate answer.
L
sixes.
D
X
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