Please see the photos for the chart and the questions. Thank you so much! First, consider an ‘experiment’ where we will toss a fair die and let X = the number of dots facing up. Of course the possible values for X are 1, 2, 3, 4, 5, and 6 and each of these is equally likely. Show the probability distribution for X using the first two columns in the table below. To avoid rounding errors, show the probabilities as fractions- not as decimals. Next fill in the next two columns. Continue using fractions instead of decimals. Don’t reduce your fractions as you’ll want to have a common denominator in each column. Express the Expected Value of X, also known as the mean, µ, as both a reduced fraction and as a decimal. E(X) = µ = ___________________________ Show your work below as you use information from the table and the appropriate formula(s) to find the variance, σ2, expressed as both a fraction and a decimal. The standard deviation is an irrational number. It would be good algebra review to express the exact value (which would include a square root) if you can. Find a decimal approximation for the standard deviation, σ (and the exact value if you wish). σ2 = ___________________________ σ ≈ ____________________________
Please see the photos for the chart and the questions. Thank you so much!
First, consider an ‘experiment’ where we will toss a fair die and let X = the number of dots facing up.
Of course the possible values for X are 1, 2, 3, 4, 5, and 6 and each of these is equally likely.
Show the probability distribution for X using the first two columns in the table below. To avoid rounding errors, show the probabilities as fractions- not as decimals.
Next fill in the next two columns. Continue using fractions instead of decimals. Don’t reduce your fractions as you’ll want to have a common denominator in each column.
Express the
E(X) = µ = ___________________________
Show your work below as you use information from the table and the appropriate formula(s) to find the variance, σ2, expressed as both a fraction and a decimal. The standard deviation is an irrational number. It would be good algebra review to express the exact value (which would include a square root) if you can. Find a decimal approximation for the standard deviation, σ (and the exact value if you wish).
σ2 = ___________________________
σ ≈ ____________________________
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