1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
yan [13]
3 years ago
9

4. A random variable X has a mean of 10 and a standard deviation of 3. If 2 is added to each value of X, what will the new mean

and standard deviation be?
Mathematics
1 answer:
Ede4ka [16]3 years ago
5 0

Adding 2 to each value of the random variable X makes a new random variable X+2. Its mean would be

E[X+2]=E[X]+E[2]=E[X]+2

since expectation is linear, and the expected value of a constant is that constant. E[X] is the mean of X, so the new mean would be

E[X+2]=10+2=12

The variance of a random variable X is

V[X]=E[X^2]-E[X]^2

so the variance of X+2 would be

V[X+2]=E[(X+2)^2]-E[X+2]^2

We already know E[X+2]=12, so simplifying above, we get

V[X+2]=E[X^2+4X+4]-12^2

V[X+2]=E[X^2]+4E[X]+4-12^2

V[X+2]=(V[X]+E[X]^2)+4E[X]-140

Standard deviation is the square root of variance, so V[X]=3^2=9.

\implies V[X+2]=(9+10^2)+4(10)-140=9

so the standard deviation remains unchanged at 3.

NB: More generally, the variance of aX+b for a,b\in\mathbb R is

V[aX+b]=a^2V[X]+b^2V[1]

but the variance of a constant is 0. In this case, a=1, so we're left with V[X+2]=V[X], as expected.

You might be interested in
Best answer or correct answer gets brainliest
Brilliant_brown [7]

Answer: C. x = 6; m∠XOY = 18

Step-by-step:

We see that ZOW and WOX are supplementary, meaning the sum of their angles equal 180.

We also know that WOY is a right angle and equals 90.

Now we can solve

180-108 = 72

90 - 72 = 18

XOY = 18

Because 3x = 18, we know that x = 18 by dividing 18 by 3

5 0
2 years ago
Pls help me on this!
ArbitrLikvidat [17]
It’s b :) haha i got it right
4 0
2 years ago
What is the answer to 3x + 16 = 14
ipn [44]
The answer is -2/3 ....
8 0
3 years ago
Read 2 more answers
Photo attached. 15 points!
notka56 [123]

your answer is A plz mark brainlies

8 0
3 years ago
Whih of the following is equivalent to (81m^6)^1/2
Setler [38]
Can you list the answer choices?

\sqrt{81m^6}   would be equivalent
4 0
3 years ago
Read 2 more answers
Other questions:
  • Let v1=(-6,4) and v2=(-3,6) compute the following.
    7·1 answer
  • P(|z|>1.96) solve this problem
    15·1 answer
  • What two numbers add to 7 and multiply to 0??
    10·2 answers
  • What is the slope-intercept form of the function described by this table?
    12·1 answer
  • What is (x squared) to the power of negative 3
    9·1 answer
  • Can someone pls help with this i need help or im finna drop out
    12·1 answer
  • Marci, Bobby, and Max began their homework at the same time. Marci finished her homework in 60 minutes. Bobby finished his homew
    9·2 answers
  • In June, Meg runs a race 10 seconds faster than she did in April. Let y represent her finishing time for the race in April. Whic
    14·2 answers
  • Imagine a couple who is ready to start a family. They plan to have exactly four children. Assuming no multiple births (twins, tr
    8·1 answer
  • On the medicine bottle it says 2 grams for a 60 lb person. the child weighs 105 lbs. how much medicine should they get?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!