how to find mgf of normal distribution?
604731
['Our object is to find the moment generating function which corresponds to. this distribution. ... ', 'Then we have a standard normal, denoted by N(z;0,1), and the corresponding. moment generating function is defined by.', '(2) Mz(t) = E(ezt) =', '∫ ezt.', '√', '2π e.']
679653
['Covariance measures the total variation of two random variables from their expected values. ... ', 'Obtain the data.', 'Calculate the mean (average) prices for each asset.', 'For each security, find the difference between each value and mean price.', 'Multiply the results obtained in the previous step.']
993544
['Kinetic Friction Formula Questions:', 'Answer: On a flat surface, the normal force on an object is η = mg. Using this, the formula can be used to find the force of friction:', 'Fk = μk η', 'Answer: On a flat surface, the normal force on an object is η = mg. ... ', 'Fk = μk η']
248171
The mean of the distribution (μx) is equal to n * P . The variance (σ2x) is n * P * ( 1 - P ). The standard deviation (σx) is sqrt[ n * P * ( 1 - P ) ].
172320
['You will use technology to calculate the p-value. ... ', 'The p-value is calculated using a t-distribution with n – 2 degrees of freedom.', 'The formula for the test statistic is t=r√n−2√1−r2 t = r n − 2 1 − r 2 . ... ', 'The p-value is the combined area in both tails.']
1378226
Calculate the F value. The F Value is calculated using the formula F = (SSE1 – SSE2 / m) / SSE2 / n-k, where SSE = residual sum of squares, m = number of restrictions and k = number of independent variables. Find the F Statistic (the critical value for this test).
1471285
['x <- c(1, 2, 3)', 'sqrt(mean(x ^ 2) - mean(x)^2)', '# [1] 0.8164966.']
7154
['Calculate the mean.', 'Subtract the mean from each observation.', 'Square each of the resulting observations.', 'Add these squared results together.', 'Divide this total by the number of observations (variance, S2).', 'Use the positive square root (standard deviation, S).']
1429186
['Compute alpha (α): α = 1 - (confidence level / 100)', 'Find the critical probability (p*): p* = 1 - α/2.', 'To express the critical value as a z-score, find the z-score having a cumulative probability equal to the critical probability (p*).', 'To express the critical value as a t statistic, follow these steps.']
202025
Step 2: Subtract the confidence level from 1, then divide by two. Step 3: Look up your answers to step 1 and 2 in the t-distribution table. For 9 degrees of freedom (df) and α = 0.025, my result is 2.262. Step 4: Divide your sample standard deviation by the square root of your sample size.
1226959
['Mean = Sum_of_each_individual/Total_number_of_items.', 'Variance = ((Original_Value – Mean)² + (Original_Value – Mean)² +.... )/(Total_number_of_items - 1)', 'Standard_Deviation = Square_root (Variance)']
259970
['t = √(2y/g)', 't = √[2*(200 m)/(9.8 m/s2)]', 't = √(40.8 s2)', 't = 6.39 s.']
27092
['Find the sample size, n, and the sample proportion. ... ', 'Multiply the sample proportion by.', 'Divide the result by n.', 'Take the square root of the calculated value. ... ', 'Multiply the result by the appropriate z*-value for the confidence level desired.']
317731
['The standard deviation formula may look confusing, but it will make sense after we break it down. ... ', 'Step 1: Find the mean.', 'Step 2: For each data point, find the square of its distance to the mean.', 'Step 3: Sum the values from Step 2.', 'Step 4: Divide by the number of data points.', 'Step 5: Take the square root.']
245669
['Estimating the standard deviation, σ, of the sample data.', 'Multiplying that number by three.', 'Adding (3 x σ to the average) for the UCL and subtracting (3 x σ from the average) for the LCL.']
260935
['RSD = Relative standard deviation.', 'S = Standard deviation.', 'x¯ = Mean of the data.']
1323921
['50(. 15) = 7.5.', '76(. 20) = 15.2.', '80(. 20) = 16.', '98(. 45) = 44.1.']