Question: Show that when and remains constant, the moment-generating function of a standardized gamma random variable approaches the moment-generating function of the

Show that when α → ∞ and β remains constant, the moment-generating function of a standardized gamma random variable approaches the moment-generating function of the standard normal distribution.

Step by Step Solution

★★★★★

3.52 Rating (162 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

M x t 1 t Mix1 In ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

583-S-J-P-D (886).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Show that when H0 is true, the mean and variance of the Wilcoxon rank sum test with sample sizes n1 and n2 are Ew)- n2 a "in2(mn2+ 1) nin2(ni +n2+1) 12 and Var w)

Let Mx(t) be the moment generating function of X, and define S(t) = log(Mx(t)). Show that syn_.EX.nd)L.var x. dt2

Use the moment generating function from Exercise 1 to verify that, if X is Geometric with parameter p, then E(X) = 1/p. In Exercise 1 P(X = x) = px(x) = (1- p)x-lp For x = 1, 2, 3,..., and pX(x) = 0...

(a) Let C=C(S,t) be a European Vanilla Call Option which depends on the underlying asset S and time t. The risk-free interest rate is r and the volatility of S is . The Payoff function of this Call...

Partial Differential Equations The Black-Scholes-Merton (BSM or just BS) PDE for the value Ct, S) of a derivative security as a function of time t and underlying asset price level S(t) = S takes the...

Question: Scientists are interested in predicting the cancer volume (in mm3) from a blood marker measurement for patients who are known to have prostate cancer. The file prostate.csv contain the...

Please help with questions 1, and make sure codes work on R Studios. Consider a location (locus) in the genome of a diploid organism where two different versions (alleles) of the DNA exist in the...

informs Vol. 34, No. 3, May-June 2004, pp. 191-205 issn 0092-2102 \u0001 eissn 1526-551X \u0001 04 \u0001 3403 \u0001 0191 doi 10.1287/inte.1030.0068 2004 INFORMS Inventory Decisions in Dell's Supply...

Given: . Probability Density Function (PDF): 0(1 -2)0-1 if0 0 is an unknown parameter. Based on these observations, determine an estimate of & using (a) maximum likelihood (b) method of moments 2....

Big Sky Outdoor Retailer sells tents for $900 each and provides a 3-year warranty for each tent. Big Sky also offers a 2-year extended warranty for an additional $100. During 2019, Big Sky sold 2,150...

1)What is the value of total assets? 2)What is the value of current liabilities? 3)Calculate the working capital? Debtors 62,000 Plant & Machinery 59,000 Bank overdraft 21,000 Cash 35,000 Motor Van...

Adjusting entries are journal entries made at the end of an accounting period for the purpose of: 1 3 ) _ _ _ _ _ _ A ) Assigning revenues to the period in which they are earned. B ) Updating related...

In the mainstream view there may be no need for a government budget deficit because: a) the intentions to save and to invest never coincide; b) the intentions to save and to invest can be quickly...

A nuclear power company is deciding whether to build a nuclear power plant at Diablo Canyon or at Roy Rogers City. The cost of building the power plant is $10 million at Diablo and $20 million at Roy...

Consider again Techwares decision problem described in Problem 40. Suppose now that Techwares utility function of net revenue x (measured in dollars), earned from the given marketing opportunities,...

Consider again the banks customer loan decision problem in Problem 51. Suppose now that the banks utility function of profit x (in dollars) is U(x) = 1 e-x/500000. Find the strategy that maximizes...

you are to hedge the market risk of a one-stock portfolio using stock index futures. Suppose today is Oct 10, 2022. On Oct 10, you purchase either 100 or 1,000 or 10,000 or 100,000 shares of you...

Washington Countys Board of Representatives is considering the construction of a longer runway at the county airport. Currently, the airport can handle only private aircraft and small commuter jets....

4 0 . 2 5 points What is the annualized standard deviation of the market ( i . e . , index ) return? ( answer in PERCENT with at least two decimal places, e . g . " 7 . 2 3 " means a 7 . 2 3 %...