If y ? -x, and every xi is i i d with a chi-squared distribution with 14 degrees of freedom, find the mgf of y m(t) = what is the distribution of y? select all that apply. there may be more than one correct answer a. chi squared(df 105) b. exponential(a 105 c. garnma(a = 2, ? = 210) d. gamma(a 1, 1/210) erponential(? = 210) f. chi-squared(df-210) g. gamma(a 105,b-2) h. garn ma(a-1, ? -1/105) i. none of the above

F. chi-squared(df-210)

Step-by-step explanation:

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

We have independent and identically distributed random chi square variables, each one with 14 degrees of freedom for . And let Y the random variable defined as :

We have a thorem that says that the distribution of Y is given by:

Proof

We need to find first the moment generating function for the random variable Y like this:

And the productory is satisfied because we have independent random variables. The moment generating function for a chi square distribution with r1 degrees of freedom is given by:

And replacing for each of the 15 distributions we got :

And using properties of algebra we got this:

And we can see that the moment generating function represent a chi square distribution with 14*15=210 degrees of freedom.  

So then the correct option is given by:

F. chi-squared(df-210)

write out the polynomial, with leading coefficient 1:

y = 1 (x+2)^1 (x-7)^1 (x-5)^2

next time, share the answer choices.   .