Answer:
a) Var[z] = 1600
D[z] = 40
b) Var[z] = 2304
D[z] = 48
c) Var[z] = 80
D[z] = 8.94
d) Var[z] = 80
D[z] = 8.94
e) Var[z] = 320
D[z] = 17.88
Step-by-step explanation:
In general
V([x+y] = V[x] + V[y] +2Cov[xy]
how in this problem Cov[XY] = 0, then
V[x+y] = V[x] + V[y]
Also we must use this properti of the variance
V[ax+b] = 
V[x]
and remember that
standard desviation = ![\sqrt{Var[x]}](https://tex.z-dn.net/?f=%5Csqrt%7BVar%5Bx%5D%7D)
a) z = 35-10x
Var[z] = 
Var[x] = 100*16 = 1600
D[z] = 
= 40
b) z = 12x -5
Var[z] = 
Var[x] = 144*16 = 2304
D[z] = 
= 48
c) z = x + y
Var[z] = Var[x+y] = Var[x] + Var[y] = 16 + 64 = 80
D[z] = 
= 8.94
d) z = x - y
Var[z] = Var[x-y] = Var[x] + Var[y] = 16 + 64 = 80
D[z] = = 8.94
e) z = -2x + 2y
Var[z] = 4Var[x] + 4Var[y] = 4*16 + 4*64 = 320
D[z] = 
= 17.88
Answer:
e. All of these statements are true.
Step-by-step explanation:
The first statement is true because an experiment is actually the process by which an observation is made. Consider rolling a die. It is called an experiment because we observe which side of the die lands facing upwards and that number is noted.
The second statement is also true because a simple event is the one which can not be further decomposed into an event. (Compound events can be decomposed into simple events).
The third statement is also true that an event is the collection of one or more simple events. An event can contain either simple events of compound events which are basically a combination of two or more simple events.
Hence, we can say that <u>all the statements are true</u>.
Domain: What are all the possible x values?
[-6, 0) U (0,2)
[ ] Closed brackets means including a number
( ) Open brackets means not including that number
Range: All possible y values
(1, 6]
