Consider the experiment where a pair of fair dice is thrown. Let X denote the random variable whose value is determined by takin
g the maximum of the spots showing on either of the two dice thrown. For example, if a 3 and a 5 were thrown, then X would take the value of Maximum(3,5) = 5. The range of values that X can assume are the positive integers {1,2,3,4,5,6}.
1. Please give the corresponding probabilities for the values of X given below.
Pr(X = 1) =
Pr(X = 2) =
Pr(X = 3) =
Pr(X = 4) =
Pr(X = 5) =
Pr(X = 6) =
2. Further, find the probability that X is divisible by 4. Probability that X is divisible by 4 = ______
1. Please give the corresponding probabilities for the values of X given below.
Pr(X = 1) =
Pr(X = 2) =
Pr(X = 3) =
Pr(X = 4) =
Pr(X = 5) =
Pr(X = 6) =
2. Further, find the probability that X is divisible by 4. Probability that X is divisible by 4 = ______
1 answer:
Answer:
1-
P(X=1) = 1/36
P(X=2) = 3/36 = 1/12
P(X=3) = 5/36
P(X=4) = 7/36
P(X=5) = 9/36 = ¼
P(X=6) = 11/36
2-
7/36
Step-by-step explanation:
1-
Attached, you will find a table with the possible values of X.
(See table attached)
As we can see, there are 36 entries so,
<em>P(X=1) = 1/36 </em>
<em> </em>
<em>P(X=2) = 3/36 = 1/12 </em>
<em> </em>
<em>P(X=3) = 5/36 </em>
<em> </em>
<em>P(X=4) = 7/36 </em>
<em> </em>
<em>P(X=5) = 9/36 = ¼ </em>
<em> </em>
<em>P(X=6) = 11/36 </em>
2-
It can be noticed that the only possible value of X which is divisible by 4 is 4 and there are 7 entries in the table, so
P(X divisible by 4) = P(X=4) = 7/36
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Alternative hypothesis:
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Step-by-step explanation:
1) Data given and notation
represent the mean for the sample
represent the standard deviation for the sample
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
2) State the null and alternative hypotheses.
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Null hypothesis:
Alternative hypothesis:
We don't know the population deviation and the sample size is lees than 30, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(1)
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3) Calculate the statistic
We can replace in formula (1) the info given like this:
4) Calculate the critical value
We need to begin calculating the degrees of freedom
The critical value for this case would be :
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Since is a one-side upper test the p value would be:
6) Conclusion
If we compare the p value and the significance level given we see that
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Answer:
Step-by-step explanation:
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