Q5. A continuous r. v. X is said to have a Gamma (a, b) distribution if its moment generating function (m. g.f.) is given by My(t) = (1 - Bt). Let X1, X 2,...,x , be a random sample of
n
72
size n from an exponential distribution with mean 1/8 and m. g.f. (1 - 01)-°. Let Y = XX,
i=1
and = 2x;. [For p. d.f. s of Gamma and Exponential, see the book or lecture notes).
i=1
(a) Find the m. g.f. My () of Y and state the distribution of Y specifying the parameters.
(b) Find the m. g.f. My(t)of X and state the distribution of X specifying the parameters.
(C) Suppose you have a random sample of size n = 100 from a Gamma (a, b) distribution
with a = 3 and B = 5/3. Use the Central Limit Theorem to find P(4.5 < X <5.5).

9x

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.

see below

step-by-step explanation:

x+2> 6

subtract 2 from each side

x+2-2 > 6-2

x > 4

there is an open circle at 4 since is it is greater than and the line goes to the right

ending amount = beginning amount / (2^n)

where "n" = number of half-lives (or elapsed time / half-life)

ending amount = 50 mg / (2 ^10 / 5.3)

ending amount = 50 mg / (2 ^ 1.8867924528)

ending amount = 50 m / 3.6981210597

ending amount = 13.5203794557 mg

or about 13.5 mg remain

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