Series expansion method of the mgf

Assignment Help Basic Statistics

Reference no: EM13243054

The continuous random variable X has probability density function (pdf) given by

493_Measure of skewness in the distribution1.png

Show that, subject to t < 1, the Moment Generator Function, MGF, of X is:

858_Measure of skewness in the distribution.png

Use the series expansion method of the MGF to find E(X), E(X²) and E(X³), the first three moments of X about the origin. Use your results to show that the mean and variance of X are both equal to 2.

The standardised third moment, b₃ = E{ (X - m)³ ÷ s³}, provides a measure of skewness in the distribution of X. Determine the value of b₃ for this distribution.

Using a suitable distributional approximation, find the probability that the mean of a random sample of n = 25 observations will exceed 2.5.

Reference no: EM13243054

Questions Cloud

Define what is its molar mass of a gas : A sample of a gas weighs 2.880 g and has a volume of 1010.0 ml at 685.0 torr and 29.0 C. What is its molar mass

Find the value of b : A rectangular coil 21cm by 37cm has 100 turns. This coil produces a maximum emf of 69V when it rotates with an angular speed of 200rad/s in a magnetic field of strength B

Define a nitrate ion as spectator ions : Write one overall equation, using an alkali metal ion and a nitrate ion as spectator ions if needed, for the following net ionic equation: H+(aq) + OH-(aq) ? H2O(l)

Evaluate the solubility product for barium fluoride : Calculate the solubility product (Ksp) for barium fluoride if the concentration of the barium ion is 3.6 x 10-3 M and of the fluoride ion is 7.2 x 10-3 M.

Series expansion method of the mgf : Provides a measure of skewness in the distribution of X. Determine the value of b3 for this distribution and using a suitable distributional approximation, find the probability that the mean of a random sample of n = 25 observations will exceed 2.5.

Examine govts role in controlling and managing health risk : Toward Effective Risk Regulations (1993) examines goverment's role in controlling and managing the health risks society faces from exposure to environmental pollution. One major problem examined in the book is cleanup of hazardous waste sites.

Find how much profit is ez sharp earning each month : EZ Sharp industries Inc manufactures the Keen Edge line of diamond abrasive cutlery sharpeners for home use. Dia Sharp holds a patent on ist unique design and can earn substantial economic profit if it prices its Keen Edge products wisely.

Find the oscillation frequency : An ideal spring is lying horizontally on a frictionless surface, find the oscillation frequency of a 2.5 kg blcok under the same circumstances

What is the value of the ratio m1/m2 : A force Farrowbold applied to an object of mass m1 produces an acceleration of 3.10 m/s2, What is the value of the ratio m1/m2

User Account

All Pages