1. The following table gives the PDF (Probability Density Function) of the discrete variable X -1 -2 2 3 4 f(x) 0.1 0.2 0.1 0.3 0.1 0.2 Calculate the E(x) (expectation) and var(x) (variance)
1. The following table gives the PDF (Probability Density Function) of the discrete variable X -1 -2 2 3 4 f(x) 0.1 0.2 0.1 0.3 0.1 0.2 Calculate the E(x) (expectation) and var(x) (variance)
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.1P
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![1. The following table gives the PDF (Probability Density Function) of the
discrete variable X
X
-1
-2
2
3
4
f(x)
0.1
0.2
0.1
0.3
0.1
0.2
Calculate the E(x) (expectation) and var(x) (variance)
2. Prove the following properties of expectation and variance:
If a and b are constants, X and Y are random variables, then
E(aX+b)=aE(x)+b
var (aX+ b) = a² var (X)
var (X+ Y)= var (X) + var (Y) +2 cov(X, Y)
=var (X) + var (Y) + 2pox0y
Of which p is correlation coefficient, oz and o, are standard error of X
and Y.
3. Assume that X- N(6, 4). What is the probability that 2 <X<10, and
what is the probability that X>10?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d5a5781-5fcd-409e-8e5b-9cd289aa8028%2F53c2acec-50f2-4b70-91d3-850ce0ccdf4a%2Fqv0s0t8_processed.png&w=3840&q=75)
Transcribed Image Text:1. The following table gives the PDF (Probability Density Function) of the
discrete variable X
X
-1
-2
2
3
4
f(x)
0.1
0.2
0.1
0.3
0.1
0.2
Calculate the E(x) (expectation) and var(x) (variance)
2. Prove the following properties of expectation and variance:
If a and b are constants, X and Y are random variables, then
E(aX+b)=aE(x)+b
var (aX+ b) = a² var (X)
var (X+ Y)= var (X) + var (Y) +2 cov(X, Y)
=var (X) + var (Y) + 2pox0y
Of which p is correlation coefficient, oz and o, are standard error of X
and Y.
3. Assume that X- N(6, 4). What is the probability that 2 <X<10, and
what is the probability that X>10?
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