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Let x1, x2...xn be independent and N(o,1) distributed. Let Sn= (X^2)1+...+(X^2)n. Show that sn is a random variable x^2-distributed with d.f=n ( use Moment generating function)
Statistics and Probability, Statistics
In order to fund her retirement, Helen needs her portfolio to have an expected return of 13.8 percent per year over the next 30 years. She has decided to invest in Stocks 1, 2, and 3, with 25 percent in Stock 1, 50 perce ...
On the below question, how did they decided the two probabilities of guessing the correct and wrong answer on a question? Where did the 0.25 and 0.75 come from? The probability of achieving exactly k successes in n t ...
Consider the following difference equation and initial condition(s). In each case, verify that the expression given for an (i) is a solution of the equation (ii) satisfies the initial condition(s). (a) an = 2(1/3)n satis ...
The computer systems department has 8 faculty, 6 are tenured. A committee is formed of 3 faculty members. If members are submitted at random: - What is the probability all members of the committee are tenured? - What is ...
What is the minimum cash flow that could be received at the end of year three to make the following project "acceptable?" Initial cost = $63,000; cash flows at end of years one and two = $35,000; opportunity cost of capi ...
Military often provides a form of qualification test for people to enter special career fields. Suppose that a large number of people have taken a test for a certain career field. Suppose that the mean of all people taki ...
Sixty percent of adults have looked at their credit score in the past six months. If you select 31 customers, what is the probability that at least 25 of them have looked at their score in the past six months?
The following data represents rain fall (x) and yield of paddy per hectare (y) in a particular area. X 113 102 95 120 140 130 125 Y 1.8 1.5 1.3 1.9 1.1 2.0 1.7 Fit the regression equation x and y. Estimate Y when x= 145. ...
Suppose that 20% of men (P=.20) and 15% of women (P= .15) are carriers of a particular genetic trait. That trait can only be inherited by a child if both parents are carriers. What is the probability that a child is born ...
The following is a partial relative frequency distribution of grades in an introductory statistics course. Grade Relative Frequency A .22 B ? C .18 D ...
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Why might a bank avoid the use of interest rate swaps, even when the institution is exposed to significant interest rate
Describe the difference between zero coupon bonds and coupon bonds. Under what conditions will a coupon bond sell at a p
Compute the present value of an annuity of $ 880 per year for 16 years, given a discount rate of 6 percent per annum. As
Compute the present value of an $1,150 payment made in ten years when the discount rate is 12 percent. (Do not round int
Compute the present value of an annuity of $ 699 per year for 19 years, given a discount rate of 6 percent per annum. As