Unit 10 - Week 8 - Expectations and Averages - Nptel

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18/05/2018 Probability Foundations for Electrical engineers - - Unit 10 - Week 8 - Expectations and Averages

https://onlinecourses.nptel.ac.in/noc18_ee01/unit?unit=104&assessment=118 1/4

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Unit 10 - Week 8 -

Expectations and Averages

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Course outline

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Week 0 - Experiments, sample space, events

Week 1 -

Probability space

Week 2 - Conditional probability

Week 3 - Independence

Week 4 - Discrete random variables

Week 5 - Conditional and joint

distributions, independence and

manipulations of random variables

Week 6- Continuous Random Variables

Week 7- Joint distributions and transformations of random variables

Week 8 -

Expectations and Averages

Expected value or mean of a random variable

Due on 2018-04-10, 23:59 IST.

1)

1 point 2)

1 point

3)

Assignment 8

The due date for submitting this assignment has passed.

Submitted assignment

Use this data for question 1 and 2

Let be a discrete random variable with p.m.f. given by the following table.

X 1 2 3 4

^p

x

^(x) 0.4 0.1 0.3 0.2 .

The mean of ____________

No, the answer is incorrect.

Score: 0

Accepted Answers:

(Type: Numeric) 2.3

The variance of =

Score: 0

Use this data for question 3 and 4

Let be a continuous random variable with p.d.f. given by

The mean of ____________

X

X =

X

X f

_X

(x) f

_X

(x) = { 5 , x

⁴

0 0 ≤ x ≤ 1,

otherwise

X =

(2)

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Properties of expectation Expectation computations for important distributions Variance Examples of variance Expectations with two random variables Correlation and covariance Examples:

Continuous distributions Examples:

Symmetry Examples:

Discrete distributions Quiz : Assignment 8 Week 8 Assignment Solution Week 8 - Feedback

1 point 4)

1 point 1 point 5)

6)

1 point 1 point 7)

No, the answer is incorrect.

Score: 0

(Type: Range) 0.831,0.835

The variance of =___________

Score: 0

(Type: Range) 0.0196,0.0200

True or False: Var =a True

False

Score: 0

False

You roll a fair die repeatedly. If it shows , you must stop. You also decide to stop if it shows a number greater than or equal to . If your score is the square of the number shown by the die on the final roll, your expected score is ___________.

No, the answer is incorrect.

Score: 0

Which of the following density functions will result in a finite mean and a finite variance?

1.

2.

3.

4.

2 only 4 only 4 and 2 1 and 3

X

(aX + b) Var(X) + b

4 1

HintHint

f (x) =

⎧

⎩

⎨ ⎪

⎪ 1 x

²

0

: x ≥ 1, : otherwise f (x) =

⎧

⎩

⎨ ⎪

⎪ 2 x

²

0

: 1 < x < 2, : otherwise f (x) = 1 : −∞ < x < ∞

π(1 + ) x

²

f (x) =

⎧

⎩

⎨ ⎪

⎪ 3 x

³

0

: x ≥ 1,

: otherwise

(3)

8)

1 point 9)

1 point 10)

1 point 11)

1 point 1 point 12)

No, the answer is incorrect.

Score: 0

2 only

Let the distribution of a random variable be given by Suppose , then Var is ______________

Score: 0

Let and be two continuous random variables with uniform in the interval and having p.d.f. for all .

Then the Cov ____________

No, the answer is incorrect.

Score: 0

(Type: Range) 6.198,6.202

Let , and . Note that the need not be

independent. The value of is ___________

Score: 0

If , the value of is ____________.

Score: 0

Twenty people, consisting of 10 married couples, are to be seated at five different tables,

with four people at each table. The twenty people are seated in a random order in the twenty chairs with

P[X = 0] = P[X = 2] = p, P[X = 1] = 1 − 2p. X

p = 0.4 [X]

X Y X [0, 1] Y

2π1

e

^{− /4π}^y²

y

(Y + X, Y − X) =

HintHint

∼ Bernoulli(0.4)

X

i

i = 1, 2, … , 6 S = ∑

i=1

6

X

i

X

i

𝔼[S]

HintHint

P( = 1, X

i

X

j

= 1) = 0.2 for i ≠ j 𝔼[ ] S

²

HintHint

(4)

each order being equally likely. What is the expected number of married couples that are seated at the same table?

20/3 20/6 30/19 34/19

No, the answer is incorrect.

Score: 0

30/19

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